diff --git a/python/paddle/fluid/framework.py b/python/paddle/fluid/framework.py
index 036e8ab30441c..db487128bbe75 100644
--- a/python/paddle/fluid/framework.py
+++ b/python/paddle/fluid/framework.py
@@ -3031,7 +3031,11 @@ def _is_inited_by(block, var):
                         # In startup_program, "c_broadcast" and "c_sync_comm_stream"
                         # are treated as initialization ops that cause error.
                         # Think of "c_broadcast" and "c_sync_comm_stream" as a special case here.
-                        if op.type in ["c_broadcast", "c_sync_comm_stream"]:
+                        # NOTE: "coalesce_tensor" is a special case for rnn with cudnn support
+                        if op.type in [
+                                "c_broadcast", "c_sync_comm_stream",
+                                "coalesce_tensor"
+                        ]:
                             continue
                         init_ops.append(op)
                 return init_ops
diff --git a/python/paddle/fluid/tests/unittests/rnn/test_rnn_cudnn_params_packing.py b/python/paddle/fluid/tests/unittests/rnn/test_rnn_cudnn_params_packing.py
new file mode 100644
index 0000000000000..0712d5be23e4b
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/rnn/test_rnn_cudnn_params_packing.py
@@ -0,0 +1,53 @@
+# Copyright (c) 2021 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.
+
+import paddle
+from unittest import TestCase
+
+
+def create_model():
+    hidden_size = 32
+    bilstm = paddle.nn.LSTM(
+        hidden_size, hidden_size, num_layers=1, direction='bidirectional')
+    return bilstm
+
+
+class TestRNNProgramClone(TestCase):
+    def setUp(self):
+        paddle.enable_static()
+
+    def test_rnn_with_cudnn_clone(self):
+        train_program = paddle.static.Program()
+        test_program = paddle.static.Program()
+        startup_prog = paddle.static.Program()
+
+        # test a typical case in static graph usage: create two nearly
+        # identical program with a shared startup program to share their
+        # parameters
+        # 
+        # when creating a parameter, the name is checked. If there is already
+        # a parameter with the same name, which is the output of a operator
+        # (i.e. its creator), its re-creation is skipped.
+        # 
+        # but if that parameter has been the output of more than one operator,
+        # an exception is raised. For special cases, white list is added.
+        # flattening rnn's parameters for the need to call cudnn kernel is such 
+        # a case.
+        with paddle.static.program_guard(train_program, startup_prog):
+            with paddle.fluid.unique_name.guard():
+                bilstm = create_model()
+
+        with paddle.fluid.program_guard(test_program, startup_prog):
+            with paddle.fluid.unique_name.guard():
+                bilstm = create_model()