diff --git a/colossalai/zero/utils/tensor_placement_policy.py b/colossalai/zero/utils/tensor_placement_policy.py
index bd962cf38..e3f3dff3d 100644
--- a/colossalai/zero/utils/tensor_placement_policy.py
+++ b/colossalai/zero/utils/tensor_placement_policy.py
@@ -1,5 +1,5 @@
 from abc import ABC, abstractmethod
-from typing import List, Optional, Dict
+from typing import List, Optional
 import torch
 from colossalai.utils import get_current_device
 from colossalai.zero.sharded_param.tensor_utils import colo_model_data_tensor_move_inline, colo_tensor_mem_usage
@@ -79,7 +79,7 @@ class AutoTensorPlacementPolicy(TensorPlacementPolicy):
                 next_compute_idx = sorted(next_compute_idx.items(), key=lambda pair: pair[1], reverse=True)
                 to_free_tensor_list = [t for (t, idx) in next_compute_idx]
             for t in to_free_tensor_list:
-                if freed_cuda_model_data > to_free_cuda_model_data:
+                if freed_cuda_model_data >= to_free_cuda_model_data:
                     break
                 freed_cuda_model_data += colo_tensor_mem_usage(t)[0]
                 colo_model_data_tensor_move_inline(t, torch.device('cpu'))
diff --git a/tests/test_zero/test_stateful_tensor_mgr.py b/tests/test_zero/test_stateful_tensor_mgr.py
index 6edefd38f..15ca1cc5c 100644
--- a/tests/test_zero/test_stateful_tensor_mgr.py
+++ b/tests/test_zero/test_stateful_tensor_mgr.py
@@ -5,7 +5,7 @@ import torch.multiprocessing as mp
 from colossalai.utils.cuda import get_current_device
 from colossalai.utils.memory_tracer import MemStatsCollector
 from colossalai.utils.memory_tracer.model_data_memtracer import GLOBAL_MODEL_DATA_TRACER
-from colossalai.utils.memory import colo_device_memory_capacity, colo_set_process_memory_fraction
+from colossalai.utils.memory import colo_set_process_memory_fraction
 from colossalai.zero.utils import StatefulTensorMgr
 from colossalai.zero.sharded_param.sharded_param import ShardedParamV2
 from colossalai.zero.sharded_param.tensorful_state import TensorState
@@ -21,18 +21,22 @@ class Net(torch.nn.Module):
 
     def __init__(self) -> None:
         super().__init__()
-        # each parameter is 512 MB
-        self.p0 = Parameter(torch.empty(1024, 1024, 128))
-        self.p1 = Parameter(torch.empty(1024, 1024, 128))
-        self.p2 = Parameter(torch.empty(1024, 1024, 128))
+        # each parameter is 128 MB
+        self.p0 = Parameter(torch.empty(1024, 1024, 32))
+        self.p1 = Parameter(torch.empty(1024, 1024, 32))
+        self.p2 = Parameter(torch.empty(1024, 1024, 32))
+
+
+def limit_cuda_memory(memory_in_g: float):
+    cuda_capacity = torch.cuda.get_device_properties(get_current_device()).total_memory
+    fraction = (memory_in_g * 1024**3) / cuda_capacity
+    colo_set_process_memory_fraction(fraction)
 
 
 def run_stm():
-    cuda_capacity = colo_device_memory_capacity(get_current_device())
-    fraction = (1.4 * 1024**3) / cuda_capacity
-    # limit max memory to 1.4GB
-    # which means only 2 parameters can be on CUDA
-    colo_set_process_memory_fraction(fraction)
+    # warmup phase use 20% CUDA memory to store params
+    # only 2 params can be on CUDA
+    limit_cuda_memory(1.26)
     model = Net()
     for p in model.parameters():
         p.colo_attr = ShardedParamV2(p, set_data_none=True)
@@ -65,6 +69,8 @@ def run_stm():
     stateful_tensor_mgr.reset()
 
     # warmup done
+    # only 2 params can be on CUDA
+    limit_cuda_memory(0.26)
     # use OPT-like eviction strategy
     apply_adjust(model, model.p0, [model.p0, model.p1], stateful_tensor_mgr)
     mem_collector.sample_model_data()
@@ -112,7 +118,7 @@ def run_dist(rank, world_size, port):
     run_stm()
 
 
-@pytest.mark.skip
+@pytest.mark.gpu
 @rerun_on_exception(exception_type=mp.ProcessRaisedException, pattern=".*Address already in use.*")
 def test_stateful_tensor_manager(world_size=1):
     run_func = partial(run_dist, world_size=world_size, port=free_port())
@@ -120,4 +126,5 @@ def test_stateful_tensor_manager(world_size=1):
 
 
 if __name__ == '__main__':
+    # this unit test can pass if available CUDA memory >= 1.5G
     test_stateful_tensor_manager()