diff --git a/pkg/scheduler/algorithm/predicates/metadata.go b/pkg/scheduler/algorithm/predicates/metadata.go
index c9d36003dde..f6180eb6f96 100644
--- a/pkg/scheduler/algorithm/predicates/metadata.go
+++ b/pkg/scheduler/algorithm/predicates/metadata.go
@@ -229,12 +229,12 @@ func getTPMapMatchingSpreadConstraints(pod *v1.Pod, nodeInfoMap map[string]*sche
 		}
 		// In accordance to design, if NodeAffinity or NodeSelector is defined,
 		// spreading is applied to nodes that pass those filters.
-		if !podMatchesNodeSelectorAndAffinityTerms(pod, node) {
+		if !PodMatchesNodeSelectorAndAffinityTerms(pod, node) {
 			return
 		}
 
 		// Ensure current node's labels contains all topologyKeys in 'constraints'.
-		if !nodeLabelsMatchSpreadConstraints(node.Labels, constraints) {
+		if !NodeLabelsMatchSpreadConstraints(node.Labels, constraints) {
 			return
 		}
 		nodeTopologyMaps := newTopologyPairsMaps()
@@ -245,7 +245,7 @@ func getTPMapMatchingSpreadConstraints(pod *v1.Pod, nodeInfoMap map[string]*sche
 				if existingPod.Namespace != pod.Namespace {
 					continue
 				}
-				ok, err := podMatchesSpreadConstraint(existingPod.Labels, constraint)
+				ok, err := PodMatchesSpreadConstraint(existingPod.Labels, constraint)
 				if err != nil {
 					errCh.SendErrorWithCancel(err, cancel)
 					return
@@ -304,10 +304,11 @@ func getHardTopologySpreadConstraints(pod *v1.Pod) (constraints []v1.TopologySpr
 	return
 }
 
-// some corner cases:
+// PodMatchesSpreadConstraint verifies if <constraint.LabelSelector> matches <podLabelSet>.
+// Some corner cases:
 // 1. podLabelSet = nil => returns (false, nil)
 // 2. constraint.LabelSelector = nil => returns (false, nil)
-func podMatchesSpreadConstraint(podLabelSet labels.Set, constraint v1.TopologySpreadConstraint) (bool, error) {
+func PodMatchesSpreadConstraint(podLabelSet labels.Set, constraint v1.TopologySpreadConstraint) (bool, error) {
 	selector, err := metav1.LabelSelectorAsSelector(constraint.LabelSelector)
 	if err != nil {
 		return false, err
@@ -318,8 +319,8 @@ func podMatchesSpreadConstraint(podLabelSet labels.Set, constraint v1.TopologySp
 	return true, nil
 }
 
-// check if ALL topology keys in spread constraints are present in node labels
-func nodeLabelsMatchSpreadConstraints(nodeLabels map[string]string, constraints []v1.TopologySpreadConstraint) bool {
+// NodeLabelsMatchSpreadConstraints checks if ALL topology keys in spread constraints are present in node labels.
+func NodeLabelsMatchSpreadConstraints(nodeLabels map[string]string, constraints []v1.TopologySpreadConstraint) bool {
 	for _, constraint := range constraints {
 		if _, ok := nodeLabels[constraint.TopologyKey]; !ok {
 			return false
@@ -388,7 +389,7 @@ func (m *topologyPairsPodSpreadMap) addPod(addedPod, preemptorPod *v1.Pod, node
 		return nil
 	}
 	constraints := getHardTopologySpreadConstraints(preemptorPod)
-	if !nodeLabelsMatchSpreadConstraints(node.Labels, constraints) {
+	if !NodeLabelsMatchSpreadConstraints(node.Labels, constraints) {
 		return nil
 	}
 
@@ -396,7 +397,7 @@ func (m *topologyPairsPodSpreadMap) addPod(addedPod, preemptorPod *v1.Pod, node
 	minMatchNeedingUpdate := make(map[string]struct{})
 	podLabelSet := labels.Set(addedPod.Labels)
 	for _, constraint := range constraints {
-		if match, err := podMatchesSpreadConstraint(podLabelSet, constraint); err != nil {
+		if match, err := PodMatchesSpreadConstraint(podLabelSet, constraint); err != nil {
 			return err
 		} else if !match {
 			continue
diff --git a/pkg/scheduler/algorithm/predicates/metadata_test.go b/pkg/scheduler/algorithm/predicates/metadata_test.go
index 911c05922bb..70d80f9fc69 100644
--- a/pkg/scheduler/algorithm/predicates/metadata_test.go
+++ b/pkg/scheduler/algorithm/predicates/metadata_test.go
@@ -904,12 +904,12 @@ func TestPodMatchesSpreadConstraint(t *testing.T) {
 	for _, tt := range tests {
 		t.Run(tt.name, func(t *testing.T) {
 			podLabelSet := labels.Set(tt.podLabels)
-			got, err := podMatchesSpreadConstraint(podLabelSet, tt.constraint)
+			got, err := PodMatchesSpreadConstraint(podLabelSet, tt.constraint)
 			if (err != nil) != tt.wantErr {
-				t.Errorf("podMatchesSpreadConstraint() error = %v, wantErr %v", err, tt.wantErr)
+				t.Errorf("PodMatchesSpreadConstraint() error = %v, wantErr %v", err, tt.wantErr)
 			}
 			if got != tt.want {
-				t.Errorf("podMatchesSpreadConstraint() = %v, want %v", got, tt.want)
+				t.Errorf("PodMatchesSpreadConstraint() = %v, want %v", got, tt.want)
 			}
 		})
 	}
diff --git a/pkg/scheduler/algorithm/predicates/predicates.go b/pkg/scheduler/algorithm/predicates/predicates.go
index 059c11220a6..2f6cbe3e76f 100644
--- a/pkg/scheduler/algorithm/predicates/predicates.go
+++ b/pkg/scheduler/algorithm/predicates/predicates.go
@@ -853,9 +853,9 @@ func nodeMatchesNodeSelectorTerms(node *v1.Node, nodeSelectorTerms []v1.NodeSele
 	return v1helper.MatchNodeSelectorTerms(nodeSelectorTerms, labels.Set(node.Labels), fields.Set(nodeFields))
 }
 
-// podMatchesNodeSelectorAndAffinityTerms checks whether the pod is schedulable onto nodes according to
+// PodMatchesNodeSelectorAndAffinityTerms checks whether the pod is schedulable onto nodes according to
 // the requirements in both NodeAffinity and nodeSelector.
-func podMatchesNodeSelectorAndAffinityTerms(pod *v1.Pod, node *v1.Node) bool {
+func PodMatchesNodeSelectorAndAffinityTerms(pod *v1.Pod, node *v1.Node) bool {
 	// Check if node.Labels match pod.Spec.NodeSelector.
 	if len(pod.Spec.NodeSelector) > 0 {
 		selector := labels.SelectorFromSet(pod.Spec.NodeSelector)
@@ -906,7 +906,7 @@ func PodMatchNodeSelector(pod *v1.Pod, meta PredicateMetadata, nodeInfo *schedul
 	if node == nil {
 		return false, nil, fmt.Errorf("node not found")
 	}
-	if podMatchesNodeSelectorAndAffinityTerms(pod, node) {
+	if PodMatchesNodeSelectorAndAffinityTerms(pod, node) {
 		return true, nil, nil
 	}
 	return false, []PredicateFailureReason{ErrNodeSelectorNotMatch}, nil
@@ -1748,7 +1748,7 @@ func EvenPodsSpreadPredicate(pod *v1.Pod, meta PredicateMetadata, nodeInfo *sche
 			return false, []PredicateFailureReason{ErrTopologySpreadConstraintsNotMatch}, nil
 		}
 
-		selfMatch, err := podMatchesSpreadConstraint(podLabelSet, constraint)
+		selfMatch, err := PodMatchesSpreadConstraint(podLabelSet, constraint)
 		if err != nil {
 			return false, nil, err
 		}
diff --git a/pkg/scheduler/algorithm/priorities/BUILD b/pkg/scheduler/algorithm/priorities/BUILD
index 42945a31811..f57986635c4 100644
--- a/pkg/scheduler/algorithm/priorities/BUILD
+++ b/pkg/scheduler/algorithm/priorities/BUILD
@@ -10,6 +10,7 @@ go_library(
     name = "go_default_library",
     srcs = [
         "balanced_resource_allocation.go",
+        "even_pods_spread.go",
         "image_locality.go",
         "interpod_affinity.go",
         "least_requested.go",
@@ -37,6 +38,7 @@ go_library(
         "//pkg/scheduler/algorithm/priorities/util:go_default_library",
         "//pkg/scheduler/api:go_default_library",
         "//pkg/scheduler/nodeinfo:go_default_library",
+        "//pkg/scheduler/util:go_default_library",
         "//pkg/util/node:go_default_library",
         "//pkg/util/parsers:go_default_library",
         "//staging/src/k8s.io/api/core/v1:go_default_library",
@@ -54,6 +56,7 @@ go_test(
     name = "go_default_test",
     srcs = [
         "balanced_resource_allocation_test.go",
+        "even_pods_spread_test.go",
         "image_locality_test.go",
         "interpod_affinity_test.go",
         "least_requested_test.go",
diff --git a/pkg/scheduler/algorithm/priorities/even_pods_spread.go b/pkg/scheduler/algorithm/priorities/even_pods_spread.go
new file mode 100644
index 00000000000..121cc032df3
--- /dev/null
+++ b/pkg/scheduler/algorithm/priorities/even_pods_spread.go
@@ -0,0 +1,209 @@
+/*
+Copyright 2019 The Kubernetes Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+package priorities
+
+import (
+	"context"
+	"math"
+	"sync/atomic"
+
+	"k8s.io/api/core/v1"
+	"k8s.io/client-go/util/workqueue"
+	"k8s.io/kubernetes/pkg/scheduler/algorithm/predicates"
+	schedulerapi "k8s.io/kubernetes/pkg/scheduler/api"
+	schedulernodeinfo "k8s.io/kubernetes/pkg/scheduler/nodeinfo"
+	schedutil "k8s.io/kubernetes/pkg/scheduler/util"
+
+	"k8s.io/klog"
+)
+
+type topologyPair struct {
+	key   string
+	value string
+}
+
+type topologySpreadConstraintsMap struct {
+	// nodeNameToPodCounts is keyed with node name, and valued with the number of matching pods.
+	nodeNameToPodCounts map[string]int64
+	// topologyPairToPodCounts is keyed with topologyPair, and valued with the number of matching pods.
+	topologyPairToPodCounts map[topologyPair]*int64
+}
+
+func newTopologySpreadConstraintsMap() *topologySpreadConstraintsMap {
+	return &topologySpreadConstraintsMap{
+		nodeNameToPodCounts:     make(map[string]int64),
+		topologyPairToPodCounts: make(map[topologyPair]*int64),
+	}
+}
+
+// Note: the <nodes> passed in are the "filtered" nodes which have passed Predicates.
+// This function iterates <nodes> to filter out the nodes which don't have required topologyKey(s),
+// and initialize two maps:
+// 1) t.topologyPairToPodCounts: keyed with both eligible topology pair and node names.
+// 2) t.nodeNameToPodCounts: keyed with node name, and valued with a *int64 pointer for eligible node only.
+func (t *topologySpreadConstraintsMap) initialize(pod *v1.Pod, nodes []*v1.Node) {
+	constraints := getSoftTopologySpreadConstraints(pod)
+	for _, node := range nodes {
+		if !predicates.NodeLabelsMatchSpreadConstraints(node.Labels, constraints) {
+			continue
+		}
+		for _, constraint := range constraints {
+			pair := topologyPair{key: constraint.TopologyKey, value: node.Labels[constraint.TopologyKey]}
+			if t.topologyPairToPodCounts[pair] == nil {
+				t.topologyPairToPodCounts[pair] = new(int64)
+			}
+		}
+		t.nodeNameToPodCounts[node.Name] = 0
+		// For those nodes which don't have all required topologyKeys present, it's intentional to keep
+		// those entries absent in nodeNameToPodCounts, so that we're able to score them to 0 afterwards.
+	}
+}
+
+// CalculateEvenPodsSpreadPriority computes a score by checking through the topologySpreadConstraints
+// that are with WhenUnsatisfiable=ScheduleAnyway (a.k.a soft constraint).
+// The function works as below:
+// 1) In all nodes, calculate the number of pods which match <pod>'s soft topology spread constraints.
+// 2) Group the number calculated in 1) by topologyPair, and sum up to corresponding candidate nodes.
+// 3) Finally normalize the number to 0~10. The node with the highest score is the most preferred.
+// Note: Symmetry is not applicable. We only weigh how incomingPod matches existingPod.
+// Whether existingPod matches incomingPod doesn't contribute to the final score.
+// This is different from the Affinity API.
+func CalculateEvenPodsSpreadPriority(pod *v1.Pod, nodeNameToInfo map[string]*schedulernodeinfo.NodeInfo, nodes []*v1.Node) (schedulerapi.HostPriorityList, error) {
+	result := make(schedulerapi.HostPriorityList, len(nodes))
+	// return if incoming pod doesn't have soft topology spread constraints.
+	constraints := getSoftTopologySpreadConstraints(pod)
+	if len(constraints) == 0 {
+		return result, nil
+	}
+
+	t := newTopologySpreadConstraintsMap()
+	t.initialize(pod, nodes)
+
+	allNodeNames := make([]string, 0, len(nodeNameToInfo))
+	for name := range nodeNameToInfo {
+		allNodeNames = append(allNodeNames, name)
+	}
+
+	errCh := schedutil.NewErrorChannel()
+	ctx, cancel := context.WithCancel(context.Background())
+	processAllNode := func(i int) {
+		nodeInfo := nodeNameToInfo[allNodeNames[i]]
+		node := nodeInfo.Node()
+		if node == nil {
+			return
+		}
+		// (1) `node` should satisfy incoming pod's NodeSelector/NodeAffinity
+		// (2) All topologyKeys need to be present in `node`
+		if !predicates.PodMatchesNodeSelectorAndAffinityTerms(pod, node) ||
+			!predicates.NodeLabelsMatchSpreadConstraints(node.Labels, constraints) {
+			return
+		}
+
+		for _, constraint := range constraints {
+			pair := topologyPair{key: constraint.TopologyKey, value: node.Labels[constraint.TopologyKey]}
+			// If current topology pair is not associated with any candidate node,
+			// continue to avoid unnecessary calculation.
+			if t.topologyPairToPodCounts[pair] == nil {
+				continue
+			}
+
+			// <matchSum> indicates how many pods (on current node) match the <constraint>.
+			matchSum := int64(0)
+			for _, existingPod := range nodeInfo.Pods() {
+				match, err := predicates.PodMatchesSpreadConstraint(existingPod.Labels, constraint)
+				if err != nil {
+					errCh.SendErrorWithCancel(err, cancel)
+					return
+				}
+				if match {
+					matchSum++
+				}
+			}
+			atomic.AddInt64(t.topologyPairToPodCounts[pair], matchSum)
+		}
+	}
+	workqueue.ParallelizeUntil(ctx, 16, len(allNodeNames), processAllNode)
+	if err := errCh.ReceiveError(); err != nil {
+		return nil, err
+	}
+
+	var minCount int64 = math.MaxInt64
+	// <total> sums up the number of matching pods on each qualified topology pair
+	var total int64
+	for _, node := range nodes {
+		if _, ok := t.nodeNameToPodCounts[node.Name]; !ok {
+			continue
+		}
+
+		// For each present <pair>, current node gets a credit of <matchSum>.
+		// And we add <matchSum> to <t.total> to reverse the final score later.
+		for _, constraint := range constraints {
+			if tpVal, ok := node.Labels[constraint.TopologyKey]; ok {
+				pair := topologyPair{key: constraint.TopologyKey, value: tpVal}
+				matchSum := *t.topologyPairToPodCounts[pair]
+				t.nodeNameToPodCounts[node.Name] += matchSum
+				total += matchSum
+			}
+		}
+		if t.nodeNameToPodCounts[node.Name] < minCount {
+			minCount = t.nodeNameToPodCounts[node.Name]
+		}
+	}
+
+	// calculate final priority score for each node
+	// TODO(Huang-Wei): in alpha version, we keep the formula as simple as possible.
+	// current version ranks the nodes properly, but it doesn't take MaxSkew into
+	// consideration, we may come up with a better formula in the future.
+	maxMinDiff := total - minCount
+	for i := range nodes {
+		node := nodes[i]
+		result[i].Host = node.Name
+
+		// debugging purpose: print the value for each node
+		// score must be pointer here, otherwise it's always 0
+		if klog.V(10) {
+			defer func(score *int, nodeName string) {
+				klog.Infof("%v -> %v: EvenPodsSpreadPriority, Score: (%d)", pod.Name, nodeName, *score)
+			}(&result[i].Score, node.Name)
+		}
+
+		if _, ok := t.nodeNameToPodCounts[node.Name]; !ok {
+			result[i].Score = 0
+			continue
+		}
+		if maxMinDiff == 0 {
+			result[i].Score = schedulerapi.MaxPriority
+			continue
+		}
+		fScore := float64(schedulerapi.MaxPriority) * (float64(total-t.nodeNameToPodCounts[node.Name]) / float64(maxMinDiff))
+		result[i].Score = int(fScore)
+	}
+
+	return result, nil
+}
+
+// TODO(Huang-Wei): combine this with getHardTopologySpreadConstraints() in predicates package
+func getSoftTopologySpreadConstraints(pod *v1.Pod) (constraints []v1.TopologySpreadConstraint) {
+	if pod != nil {
+		for _, constraint := range pod.Spec.TopologySpreadConstraints {
+			if constraint.WhenUnsatisfiable == v1.ScheduleAnyway {
+				constraints = append(constraints, constraint)
+			}
+		}
+	}
+	return
+}
diff --git a/pkg/scheduler/algorithm/priorities/even_pods_spread_test.go b/pkg/scheduler/algorithm/priorities/even_pods_spread_test.go
new file mode 100644
index 00000000000..b7da0dbe69d
--- /dev/null
+++ b/pkg/scheduler/algorithm/priorities/even_pods_spread_test.go
@@ -0,0 +1,537 @@
+/*
+Copyright 2019 The Kubernetes Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+package priorities
+
+import (
+	"fmt"
+	"reflect"
+	"testing"
+
+	"k8s.io/api/core/v1"
+	schedulerapi "k8s.io/kubernetes/pkg/scheduler/api"
+	schedulernodeinfo "k8s.io/kubernetes/pkg/scheduler/nodeinfo"
+	st "k8s.io/kubernetes/pkg/scheduler/testing"
+)
+
+func Test_topologySpreadConstraintsMap_initialize(t *testing.T) {
+	tests := []struct {
+		name                string
+		pod                 *v1.Pod
+		nodes               []*v1.Node
+		wantNodeNameMap     map[string]int64
+		wantTopologyPairMap map[topologyPair]*int64
+	}{
+		{
+			name: "normal case",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("zone", "zone1").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("zone", "zone1").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-x").Label("zone", "zone2").Label("node", "node-x").Obj(),
+			},
+			wantNodeNameMap: map[string]int64{
+				"node-a": 0,
+				"node-b": 0,
+				"node-x": 0,
+			},
+			wantTopologyPairMap: map[topologyPair]*int64{
+				{key: "zone", value: "zone1"}:  new(int64),
+				{key: "zone", value: "zone2"}:  new(int64),
+				{key: "node", value: "node-a"}: new(int64),
+				{key: "node", value: "node-b"}: new(int64),
+				{key: "node", value: "node-x"}: new(int64),
+			},
+		},
+		{
+			name: "node-x doesn't have label zone",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("bar").Obj()).
+				Obj(),
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("zone", "zone1").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("zone", "zone1").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-x").Label("node", "node-x").Obj(),
+			},
+			wantNodeNameMap: map[string]int64{
+				"node-a": 0,
+				"node-b": 0,
+			},
+			wantTopologyPairMap: map[topologyPair]*int64{
+				{key: "zone", value: "zone1"}:  new(int64),
+				{key: "node", value: "node-a"}: new(int64),
+				{key: "node", value: "node-b"}: new(int64),
+			},
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			tMap := newTopologySpreadConstraintsMap()
+			tMap.initialize(tt.pod, tt.nodes)
+			if !reflect.DeepEqual(tMap.nodeNameToPodCounts, tt.wantNodeNameMap) {
+				t.Errorf("initilize().nodeNameToPodCounts = %#v, want %#v", tMap.nodeNameToPodCounts, tt.wantNodeNameMap)
+			}
+			if !reflect.DeepEqual(tMap.topologyPairToPodCounts, tt.wantTopologyPairMap) {
+				t.Errorf("initilize().topologyPairToPodCounts = %#v, want %#v", tMap.topologyPairToPodCounts, tt.wantTopologyPairMap)
+			}
+		})
+	}
+}
+
+func TestCalculateEvenPodsSpreadPriority(t *testing.T) {
+	tests := []struct {
+		name         string
+		pod          *v1.Pod
+		existingPods []*v1.Pod
+		nodes        []*v1.Node
+		failedNodes  []*v1.Node // nodes + failedNodes = all nodes
+		want         schedulerapi.HostPriorityList
+	}{
+		// Explanation on the Legend:
+		// a) X/Y means there are X matching pods on node1 and Y on node2, both nodes are candidates
+		//   (i.e. they have passed all predicates)
+		// b) X/~Y~ means there are X matching pods on node1 and Y on node2, but node Y is NOT a candidate
+		// c) X/?Y? means there are X matching pods on node1 and Y on node2, both nodes are candidates
+		//    but node2 either i) doesn't have all required topologyKeys present, or ii) doesn't match
+		//    incoming pod's nodeSelector/nodeAffinity
+		{
+			// if there is only one candidate node, it should be scored to 10
+			name: "one constraint on node, no existing pods",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("node", "node-b").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 10},
+				{Host: "node-b", Score: 10},
+			},
+		},
+		{
+			// if there is only one candidate node, it should be scored to 10
+			name: "one constraint on node, only one node is candidate",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a2").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("node", "node-a").Obj(),
+			},
+			failedNodes: []*v1.Node{
+				st.MakeNode().Name("node-b").Label("node", "node-b").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 10},
+			},
+		},
+		{
+			name: "one constraint on node, all nodes have the same number of matching pods",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("node", "node-b").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 10},
+				{Host: "node-b", Score: 10},
+			},
+		},
+		{
+			// matching pods spread as 2/1/0/3, total = 6
+			// after reversing, it's 4/5/6/3
+			// so scores = 40/6, 50/6, 60/6, 30/6
+			name: "one constraint on node, all 4 nodes are candidates",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a2").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-d1").Node("node-d").Label("foo", "").Obj(),
+				st.MakePod().Name("p-d2").Node("node-d").Label("foo", "").Obj(),
+				st.MakePod().Name("p-d3").Node("node-d").Label("foo", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-c").Label("node", "node-c").Obj(),
+				st.MakeNode().Name("node-d").Label("node", "node-d").Obj(),
+			},
+			failedNodes: []*v1.Node{},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 6},
+				{Host: "node-b", Score: 8},
+				{Host: "node-c", Score: 10},
+				{Host: "node-d", Score: 5},
+			},
+		},
+		{
+			// matching pods spread as 4/2/1/~3~, total = 4+2+1 = 7 (as node4 is not a candidate)
+			// after reversing, it's 3/5/6
+			// so scores = 30/6, 50/6, 60/6
+			name: "one constraint on node, 3 out of 4 nodes are candidates",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a2").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a3").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a4").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b2").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-x1").Node("node-x").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y1").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y2").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y3").Node("node-y").Label("foo", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-x").Label("node", "node-x").Obj(),
+			},
+			failedNodes: []*v1.Node{
+				st.MakeNode().Name("node-y").Label("node", "node-y").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 5},
+				{Host: "node-b", Score: 8},
+				{Host: "node-x", Score: 10},
+			},
+		},
+		{
+			// matching pods spread as 4/?2?/1/~3~, total = 4+?+1 = 5 (as node2 is problematic)
+			// after reversing, it's 1/?/4
+			// so scores = 10/4, 0, 40/4
+			name: "one constraint on node, 3 out of 4 nodes are candidates",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a2").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a3").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a4").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b2").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-x1").Node("node-x").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y1").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y2").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y3").Node("node-y").Label("foo", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("n", "node-b").Obj(), // label `n` doesn't match topologyKey
+				st.MakeNode().Name("node-x").Label("node", "node-x").Obj(),
+			},
+			failedNodes: []*v1.Node{
+				st.MakeNode().Name("node-y").Label("node", "node-y").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 2},
+				{Host: "node-b", Score: 0},
+				{Host: "node-x", Score: 10},
+			},
+		},
+		{
+			// matching pods spread as 4/2/1/~3~, total = 6+6+4 = 16 (as topologyKey is zone instead of node)
+			// after reversing, it's 10/10/12
+			// so scores = 100/12, 100/12, 120/12
+			name: "one constraint on zone, 3 out of 4 nodes are candidates",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a2").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a3").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a4").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b2").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-x1").Node("node-x").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y1").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y2").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y3").Node("node-y").Label("foo", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("zone", "zone1").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("zone", "zone1").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-x").Label("zone", "zone2").Label("node", "node-x").Obj(),
+			},
+			failedNodes: []*v1.Node{
+				st.MakeNode().Name("node-y").Label("zone", "zone2").Label("node", "node-y").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 8},
+				{Host: "node-b", Score: 8},
+				{Host: "node-x", Score: 10},
+			},
+		},
+		{
+			// matching pods spread as 2/~1~/2/~4~, total = 2+3 + 2+6 = 13 (zone and node should be both summed up)
+			// after reversing, it's 8/5
+			// so scores = 80/8, 50/8
+			name: "two constraints on zone and node, 2 out of 4 nodes are candidates",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-a2").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Obj(),
+				st.MakePod().Name("p-x1").Node("node-x").Label("foo", "").Obj(),
+				st.MakePod().Name("p-x2").Node("node-x").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y1").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y2").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y3").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y4").Node("node-y").Label("foo", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("zone", "zone1").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-x").Label("zone", "zone2").Label("node", "node-x").Obj(),
+			},
+			failedNodes: []*v1.Node{
+				st.MakeNode().Name("node-b").Label("zone", "zone1").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-y").Label("zone", "zone2").Label("node", "node-y").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 10},
+				{Host: "node-x", Score: 6},
+			},
+		},
+		{
+			// If constraints hold different labelSelectors, it's a little complex.
+			// +----------------------+------------------------+
+			// |         zone1        |          zone2         |
+			// +----------------------+------------------------+
+			// | node-a |    node-b   | node-x |     node-y    |
+			// +--------+-------------+--------+---------------+
+			// | P{foo} | P{foo, bar} |        | P{foo} P{bar} |
+			// +--------+-------------+--------+---------------+
+			// For the first constraint (zone): the matching pods spread as 2/2/1/1
+			// For the second constraint (node): the matching pods spread as 0/1/0/1
+			// sum them up gets: 2/3/1/2, and total number is 8.
+			// after reversing, it's 6/5/7/6
+			// so scores = 60/7, 50/7, 70/7, 60/7
+			name: "two constraints on zone and node, with different labelSelectors",
+			pod: st.MakePod().Name("p").Label("foo", "").Label("bar", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("bar").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Label("bar", "").Obj(),
+				st.MakePod().Name("p-y1").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y2").Node("node-y").Label("bar", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("zone", "zone1").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("zone", "zone1").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-x").Label("zone", "zone2").Label("node", "node-x").Obj(),
+				st.MakeNode().Name("node-y").Label("zone", "zone2").Label("node", "node-y").Obj(),
+			},
+			failedNodes: []*v1.Node{},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 8},
+				{Host: "node-b", Score: 7},
+				{Host: "node-x", Score: 10},
+				{Host: "node-y", Score: 8},
+			},
+		},
+		{
+			// For the first constraint (zone): the matching pods spread as 0/0/2/2
+			// For the second constraint (node): the matching pods spread as 0/1/0/1
+			// sum them up gets: 0/1/2/3, and total number is 6.
+			// after reversing, it's 6/5/4/3.
+			// so scores = 60/6, 50/6, 40/6, 30/6
+			name: "two constraints on zone and node, with different labelSelectors, some nodes have 0 pods",
+			pod: st.MakePod().Name("p").Label("foo", "").Label("bar", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("bar").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-b1").Node("node-b").Label("bar", "").Obj(),
+				st.MakePod().Name("p-x1").Node("node-x").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y1").Node("node-y").Label("foo", "").Label("bar", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("zone", "zone1").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("zone", "zone1").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-x").Label("zone", "zone2").Label("node", "node-x").Obj(),
+				st.MakeNode().Name("node-y").Label("zone", "zone2").Label("node", "node-y").Obj(),
+			},
+			failedNodes: []*v1.Node{},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 10},
+				{Host: "node-b", Score: 8},
+				{Host: "node-x", Score: 6},
+				{Host: "node-y", Score: 5},
+			},
+		},
+		{
+			// For the first constraint (zone): the matching pods spread as 2/2/1/~1~
+			// For the second constraint (node): the matching pods spread as 0/1/0/~1~
+			// sum them up gets: 2/3/1, and total number is 6.
+			// after reversing, it's 4/3/5
+			// so scores = 40/5, 30/5, 50/5
+			name: "two constraints on zone and node, with different labelSelectors, 3 out of 4 nodes are candidates",
+			pod: st.MakePod().Name("p").Label("foo", "").Label("bar", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("bar").Obj()).
+				Obj(),
+			existingPods: []*v1.Pod{
+				st.MakePod().Name("p-a1").Node("node-a").Label("foo", "").Obj(),
+				st.MakePod().Name("p-b1").Node("node-b").Label("foo", "").Label("bar", "").Obj(),
+				st.MakePod().Name("p-y1").Node("node-y").Label("foo", "").Obj(),
+				st.MakePod().Name("p-y2").Node("node-y").Label("bar", "").Obj(),
+			},
+			nodes: []*v1.Node{
+				st.MakeNode().Name("node-a").Label("zone", "zone1").Label("node", "node-a").Obj(),
+				st.MakeNode().Name("node-b").Label("zone", "zone1").Label("node", "node-b").Obj(),
+				st.MakeNode().Name("node-x").Label("zone", "zone2").Label("node", "node-x").Obj(),
+			},
+			failedNodes: []*v1.Node{
+				st.MakeNode().Name("node-y").Label("zone", "zone2").Label("node", "node-y").Obj(),
+			},
+			want: []schedulerapi.HostPriority{
+				{Host: "node-a", Score: 8},
+				{Host: "node-b", Score: 6},
+				{Host: "node-x", Score: 10},
+			},
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			allNodes := append([]*v1.Node{}, tt.nodes...)
+			allNodes = append(allNodes, tt.failedNodes...)
+			nodeNameToInfo := schedulernodeinfo.CreateNodeNameToInfoMap(tt.existingPods, allNodes)
+
+			got, _ := CalculateEvenPodsSpreadPriority(tt.pod, nodeNameToInfo, tt.nodes)
+			if !reflect.DeepEqual(got, tt.want) {
+				t.Errorf("CalculateEvenPodsSpreadPriority() = %#v, want %#v", got, tt.want)
+			}
+		})
+	}
+}
+
+func makeNodesAndPods(pod *v1.Pod, existingPodsNum, allNodesNum, filteredNodesNum int) (existingPods []*v1.Pod, allNodes []*v1.Node, filteredNodes []*v1.Node) {
+	var topologyKeys []string
+	var labels []string
+	// regions := 3
+	zones := 10
+	for _, c := range pod.Spec.TopologySpreadConstraints {
+		topologyKeys = append(topologyKeys, c.TopologyKey)
+		labels = append(labels, c.LabelSelector.MatchExpressions[0].Key)
+	}
+	// build nodes
+	for i := 0; i < allNodesNum; i++ {
+		nodeWrapper := st.MakeNode().Name(fmt.Sprintf("node%d", i))
+		for _, tpKey := range topologyKeys {
+			if tpKey == "zone" {
+				nodeWrapper = nodeWrapper.Label("zone", fmt.Sprintf("zone%d", i%zones))
+			} else if tpKey == "node" {
+				nodeWrapper = nodeWrapper.Label("node", fmt.Sprintf("node%d", i))
+			}
+		}
+		node := nodeWrapper.Obj()
+		allNodes = append(allNodes, node)
+		if len(filteredNodes) < filteredNodesNum {
+			filteredNodes = append(filteredNodes, node)
+		}
+	}
+	// build pods
+	for i := 0; i < existingPodsNum; i++ {
+		podWrapper := st.MakePod().Name(fmt.Sprintf("pod%d", i)).Node(fmt.Sprintf("node%d", i%allNodesNum))
+		// apply labels[0], labels[0,1], ..., labels[all] to each pod in turn
+		for _, label := range labels[:i%len(labels)+1] {
+			podWrapper = podWrapper.Label(label, "")
+		}
+		existingPods = append(existingPods, podWrapper.Obj())
+	}
+	return
+}
+
+func BenchmarkTestCalculateEvenPodsSpreadPriority(b *testing.B) {
+	tests := []struct {
+		name             string
+		pod              *v1.Pod
+		existingPodsNum  int
+		allNodesNum      int
+		filteredNodesNum int
+	}{
+		{
+			name: "1000nodes/single-constraint-zone",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPodsNum:  10000,
+			allNodesNum:      1000,
+			filteredNodesNum: 500,
+		},
+		{
+			name: "1000nodes/single-constraint-node",
+			pod: st.MakePod().Name("p").Label("foo", "").
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				Obj(),
+			existingPodsNum:  10000,
+			allNodesNum:      1000,
+			filteredNodesNum: 500,
+		},
+		{
+			name: "1000nodes/two-constraints-zone-node",
+			pod: st.MakePod().Name("p").Label("foo", "").Label("bar", "").
+				SpreadConstraint(1, "zone", softSpread, st.MakeLabelSelector().Exists("foo").Obj()).
+				SpreadConstraint(1, "node", softSpread, st.MakeLabelSelector().Exists("bar").Obj()).
+				Obj(),
+			existingPodsNum:  10000,
+			allNodesNum:      1000,
+			filteredNodesNum: 500,
+		},
+	}
+	for _, tt := range tests {
+		b.Run(tt.name, func(b *testing.B) {
+			existingPods, allNodes, filteredNodes := makeNodesAndPods(tt.pod, tt.existingPodsNum, tt.allNodesNum, tt.filteredNodesNum)
+			nodeNameToInfo := schedulernodeinfo.CreateNodeNameToInfoMap(existingPods, allNodes)
+			b.ResetTimer()
+			for i := 0; i < b.N; i++ {
+				CalculateEvenPodsSpreadPriority(tt.pod, nodeNameToInfo, filteredNodes)
+			}
+		})
+	}
+}
+
+var (
+	hardSpread = v1.DoNotSchedule
+	softSpread = v1.ScheduleAnyway
+)
diff --git a/pkg/scheduler/algorithm/priorities/priorities.go b/pkg/scheduler/algorithm/priorities/priorities.go
index 605fdd143e3..5c2d76b94de 100644
--- a/pkg/scheduler/algorithm/priorities/priorities.go
+++ b/pkg/scheduler/algorithm/priorities/priorities.go
@@ -51,4 +51,7 @@ const (
 	ImageLocalityPriority = "ImageLocalityPriority"
 	// ResourceLimitsPriority defines the nodes of prioritizer function ResourceLimitsPriority.
 	ResourceLimitsPriority = "ResourceLimitsPriority"
+	// EvenPodsSpreadPriority defines the name of prioritizer function that prioritizes nodes
+	// which have pods and labels matching the incoming pod's topologySpreadConstraints.
+	EvenPodsSpreadPriority = "EvenPodsSpreadPriority"
 )
diff --git a/pkg/scheduler/algorithmprovider/defaults/defaults.go b/pkg/scheduler/algorithmprovider/defaults/defaults.go
index a77ee69e069..6fd14d4513f 100644
--- a/pkg/scheduler/algorithmprovider/defaults/defaults.go
+++ b/pkg/scheduler/algorithmprovider/defaults/defaults.go
@@ -87,10 +87,15 @@ func ApplyFeatureGates() {
 		klog.Infof("TaintNodesByCondition is enabled, PodToleratesNodeTaints predicate is mandatory")
 	}
 
-	// Only register EvenPodsSpreadPredicate if the feature is enabled
+	// Only register EvenPodsSpread predicate & priority if the feature is enabled
 	if utilfeature.DefaultFeatureGate.Enabled(features.EvenPodsSpread) {
+		klog.Infof("Registering EvenPodsSpread predicate and priority function")
+		// register predicate
 		factory.InsertPredicateKeyToAlgorithmProviderMap(predicates.EvenPodsSpreadPred)
 		factory.RegisterFitPredicate(predicates.EvenPodsSpreadPred, predicates.EvenPodsSpreadPredicate)
+		// register priority
+		factory.InsertPriorityKeyToAlgorithmProviderMap(priorities.EvenPodsSpreadPriority)
+		factory.RegisterPriorityFunction(priorities.EvenPodsSpreadPriority, priorities.CalculateEvenPodsSpreadPriority, 1)
 	}
 
 	// Prioritizes nodes that satisfy pod's resource limits