diff --git a/python/paddle/fluid/tests/unittests/test_imperative_partitial_backward.py b/python/paddle/fluid/tests/unittests/test_imperative_partitial_backward.py
new file mode 100644
index 0000000000000000000000000000000000000000..c6a2ad9e3d5ce79298160bdca2506c989f356ce0
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_imperative_partitial_backward.py
@@ -0,0 +1,53 @@
+# Copyright (c) 2019 PaddlePaddle Authors. All Rights Reserved.
+#
+# 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.
+
+from __future__ import print_function
+
+import unittest
+import paddle.fluid as fluid
+import numpy as np
+
+
+class TestImperativePartitialBackward(unittest.TestCase):
+    def test_partitial_backward(self):
+        with fluid.dygraph.guard():
+            x = np.random.randn(2, 4, 5).astype("float32")
+            x = fluid.dygraph.to_variable(x)
+            fc1 = fluid.dygraph.FC("fc1", 10, num_flatten_dims=2)
+            fc2 = fluid.dygraph.FC("fc2", 10, num_flatten_dims=2)
+
+            y = fc1(x[:, :2])
+            z = fc2(x[:, 2:])
+            loss = fluid.layers.reduce_mean(y)
+            loss.backward()
+
+            for param in fc1.parameters():
+                self.assertIsNotNone(param._ivar._grad_ivar())
+
+            for param in fc2.parameters():
+                self.assertIsNone(param._ivar._grad_ivar())
+
+            optimizer = fluid.optimizer.AdamOptimizer()
+            _, params_grads = optimizer.minimize(loss)
+
+            self.assertListEqual(
+                sorted([p.name for p in fc1.parameters()]),
+                sorted([p_g[0].name for p_g in params_grads]))
+
+            fc1.clear_gradients()
+            fc2.clear_gradients()
+
+
+if __name__ == '__main__':
+    unittest.main()