diff --git a/test/e2e_kubeadm/admin_test.go b/test/e2e_kubeadm/admin_test.go
new file mode 100644
index 00000000000..bb49b3973d2
--- /dev/null
+++ b/test/e2e_kubeadm/admin_test.go
@@ -0,0 +1,91 @@
+/*
+Copyright 2023 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 kubeadm
+
+import (
+	"context"
+
+	"github.com/onsi/ginkgo/v2"
+
+	rbacv1 "k8s.io/api/rbac/v1"
+	"k8s.io/apimachinery/pkg/util/version"
+	admissionapi "k8s.io/pod-security-admission/api"
+
+	"k8s.io/kubernetes/test/e2e/framework"
+	e2eskipper "k8s.io/kubernetes/test/e2e/framework/skipper"
+)
+
+const (
+	kubeadmClusterAdminsGroupAndCRB = "kubeadm:cluster-admins"
+	clusterAdminClusterRole         = "cluster-admin"
+)
+
+// Define a container for all the tests aimed at verifying that administrators
+// have "cluster-admin" level of access.
+var _ = Describe("admin", func() {
+
+	// Get an instance of the k8s test framework
+	f := framework.NewDefaultFramework("admin")
+	f.NamespacePodSecurityLevel = admissionapi.LevelPrivileged
+
+	// Tests in this container are not expected to create new objects in the cluster
+	// so we are disabling the creation of a namespace in order to get a faster execution
+	f.SkipNamespaceCreation = true
+
+	ginkgo.It("kubeadm:cluster-admins CRB must exist and be binding the cluster-admin ClusterRole"+
+		" to the kubeadm:cluster-admins Group", func(ctx context.Context) {
+
+		// Use the ClusterConfiguration.kubernetesVersion to decide whether to look for the CRB.
+		// It was added in kubeadm v1.29-pre, but kubeadm supports a maximum skew of N-1
+		// with the control plane, so this is fine as long as kubernetesVersion matches
+		// the kubeadm version. Otherwise this test is skipped.
+		m := getClusterConfiguration(f.ClientSet)
+		const verKey = "kubernetesVersion"
+		verInterface, exists := m[verKey]
+		if !exists {
+			framework.Failf("the kubeadm ConfigMap %s is missing a %s key in %s",
+				kubeadmConfigName,
+				verKey,
+				kubeadmConfigClusterConfigurationConfigMapKey)
+		}
+
+		// Parse the version string
+		verStr, ok := verInterface.(string)
+		if !ok {
+			framework.Failf("cannot cast %s to string", verKey)
+		}
+		ver, err := version.ParseSemantic(verStr)
+		if err != nil {
+			framework.Failf("could not parse the %s key: %v", verKey, err)
+		}
+
+		// If the version is older than the version when this feature was added, skip this test
+		minVer := version.MustParseSemantic("v1.29.0-alpha.2.188+05076de57fc49f")
+		if !ver.AtLeast(minVer) {
+			e2eskipper.Skipf("Skipping because version %s is older than the minimum version %s",
+				ver,
+				minVer)
+		}
+
+		// Expect the CRB to exist
+		ExpectClusterRoleBindingWithSubjectAndRole(f.ClientSet,
+			kubeadmClusterAdminsGroupAndCRB,
+			rbacv1.GroupKind, kubeadmClusterAdminsGroupAndCRB,
+			clusterAdminClusterRole,
+		)
+	})
+})