diff --git a/python/paddle/tensor/math.py b/python/paddle/tensor/math.py
index cf956083d6b7b..302bafc087929 100644
--- a/python/paddle/tensor/math.py
+++ b/python/paddle/tensor/math.py
@@ -2057,7 +2057,16 @@ def __check_input(x, y):
             var_names = {'x': x, 'y': y}
             for name, val in var_names.items():
                 check_variable_and_dtype(
-                    val, name, ['float16', 'float32', 'float64'], 'mm'
+                    val,
+                    name,
+                    [
+                        'float16',
+                        'float32',
+                        'float64',
+                        'complex64',
+                        'complex128',
+                    ],
+                    'mm',
                 )
             x_shape = list(x.shape)
             y_shape = list(y.shape)
diff --git a/test/legacy_test/test_matmul_op.py b/test/legacy_test/test_matmul_op.py
index b5ac23f3e38ad..648e38b90cea8 100644
--- a/test/legacy_test/test_matmul_op.py
+++ b/test/legacy_test/test_matmul_op.py
@@ -202,6 +202,51 @@ def test_dygraph_without_out(self):
         np.testing.assert_allclose(expected_result, out.numpy(), rtol=1e-05)
 
 
+class API_TestMm_complex64(unittest.TestCase):
+    def test_out_complex64(self):
+        with paddle_static_guard():
+            with fluid.program_guard(fluid.Program()):
+                x = paddle.static.data(name="x", shape=[2], dtype="complex64")
+                y = paddle.static.data(name='y', shape=[2], dtype='complex64')
+                result = paddle.mm(x, y)
+                exe = fluid.Executor(fluid.CPUPlace())
+                data1 = (np.random.rand(2) + 1j * np.random.rand(2)).astype(
+                    "complex64"
+                )
+                data2 = (np.random.rand(2) + 1j * np.random.rand(2)).astype(
+                    "complex64"
+                )
+                np_res = exe.run(
+                    feed={'x': data1, 'y': data2}, fetch_list=[result]
+                )
+                expected_result = np.matmul(data1, data2)
+
+            np.testing.assert_allclose(
+                np_res,
+                expected_result,
+                rtol=1e-05,
+                atol=1e-05,
+                err_msg='two value is            {}\n{}, check diff!'.format(
+                    np_res, expected_result
+                ),
+            )
+
+    def test_dygraph_without_out_complex64(self):
+        device = fluid.CPUPlace()
+        with fluid.dygraph.guard(device):
+            input_array1 = np.random.rand(3, 4).astype(
+                "complex64"
+            ) + 1j * np.random.rand(3, 4).astype("complex64")
+            input_array2 = np.random.rand(4, 3).astype(
+                "complex64"
+            ) + 1j * np.random.rand(4, 3).astype("complex64")
+            data1 = fluid.dygraph.to_variable(input_array1)
+            data2 = fluid.dygraph.to_variable(input_array2)
+            out = paddle.mm(data1, data2)
+            expected_result = np.matmul(input_array1, input_array2)
+        np.testing.assert_allclose(expected_result, out.numpy(), rtol=1e-05)
+
+
 class Test_API_Matmul(unittest.TestCase):
     def test_dygraph_without_out(self):
         device = fluid.CPUPlace()