diff --git a/python/paddle/fluid/tests/unittests/test_log1p_op.py b/python/paddle/fluid/tests/unittests/test_log1p_op.py
new file mode 100644
index 0000000000000..9af95649f8450
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_log1p_op.py
@@ -0,0 +1,38 @@
+#   Copyright (c) 2018 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 unittest
+
+import paddle
+import paddle.fluid.core as core
+import paddle.static as static
+
+
+class Test_Log1p_Op_Fp16(unittest.TestCase):
+    def test_api_fp16(self):
+        paddle.enable_static()
+        with static.program_guard(static.Program(), static.Program()):
+            x = [[2, 3, 4], [7, 8, 9]]
+            x = paddle.to_tensor(x, dtype='float16')
+            out = paddle.log1p(x)
+            if core.is_compiled_with_cuda():
+                place = paddle.CUDAPlace(0)
+                exe = static.Executor(place)
+                (res,) = exe.run(fetch_list=[out])
+
+
+if __name__ == '__main__':
+    paddle.enable_static()
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/test_log_op.py b/python/paddle/fluid/tests/unittests/test_log_op.py
new file mode 100644
index 0000000000000..4e15cccc3e25c
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_log_op.py
@@ -0,0 +1,38 @@
+#   Copyright (c) 2018 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 unittest
+
+import paddle
+import paddle.fluid.core as core
+import paddle.static as static
+
+
+class Test_Log_Op_Fp16(unittest.TestCase):
+    def test_api_fp16(self):
+        paddle.enable_static()
+        with static.program_guard(static.Program(), static.Program()):
+            x = [[2, 3, 4], [7, 8, 9]]
+            x = paddle.to_tensor(x, dtype='float16')
+            out = paddle.log(x)
+            if core.is_compiled_with_cuda():
+                place = paddle.CUDAPlace(0)
+                exe = static.Executor(place)
+                (res,) = exe.run(fetch_list=[out])
+
+
+if __name__ == '__main__':
+    paddle.enable_static()
+    unittest.main()
diff --git a/python/paddle/tensor/math.py b/python/paddle/tensor/math.py
index 9e7c04be8fca9..923a5322308bb 100644
--- a/python/paddle/tensor/math.py
+++ b/python/paddle/tensor/math.py
@@ -135,7 +135,7 @@ def log(x, name=None):
         Out = \ln(x)
 
     Args:
-        x (Tensor): Input Tensor. Must be one of the following types: float32, float64.
+        x (Tensor): Input Tensor. Must be one of the following types: float16, float32, float64.
         name (str|None): The default value is None. Normally there is no need for user to set this property. For more information, please refer to :ref:`api_guide_Name`
 
 
@@ -156,7 +156,9 @@ def log(x, name=None):
     if in_dygraph_mode():
         return _C_ops.log(x)
     else:
-        check_variable_and_dtype(x, 'x', ['float32', 'float64'], "log")
+        check_variable_and_dtype(
+            x, 'x', ['float16', 'float32', 'float64'], "log"
+        )
         inputs = {'X': [x]}
         helper = LayerHelper('log', **locals())
         dtype = helper.input_dtype(input_param_name='x')
@@ -2127,7 +2129,7 @@ def logsumexp(x, axis=None, keepdim=False, name=None):
        logsumexp(x) = \log\sum exp(x)
 
     Args:
-        x (Tensor): The input Tensor with data type float32 or float64, which
+        x (Tensor): The input Tensor with data type float16, float32 or float64, which
             have no more than 4 dimensions.
         axis (int|list|tuple, optional): The axis along which to perform
             logsumexp calculations. ``axis`` should be int, list(int) or
@@ -2166,7 +2168,9 @@ def logsumexp(x, axis=None, keepdim=False, name=None):
     if in_dygraph_mode():
         return _C_ops.logsumexp(x, axis, keepdim, reduce_all)
     else:
-        check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'logsumexp')
+        check_variable_and_dtype(
+            x, 'x', ['float16', 'float32', 'float64'], 'logsumexp'
+        )
 
         helper = LayerHelper('logsumexp', **locals())
         attrs = {'axis': axis, 'keepdim': keepdim, 'reduce_all': reduce_all}
@@ -2648,7 +2652,7 @@ def log1p(x, name=None):
         Out = \ln(x+1)
 
     Args:
-        x (Tensor): Input Tensor. Must be one of the following types: float32, float64.
+        x (Tensor): Input Tensor. Must be one of the following types: float16, float32, float64.
         name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
 
     Returns:
@@ -2667,7 +2671,9 @@ def log1p(x, name=None):
     if in_dygraph_mode():
         return _C_ops.log1p(x)
     else:
-        check_variable_and_dtype(x, 'x', ['float32', 'float64'], "log1p")
+        check_variable_and_dtype(
+            x, 'x', ['float16', 'float32', 'float64'], "log1p"
+        )
         inputs = {'X': [x]}
         helper = LayerHelper('log1p', **locals())
         dtype = helper.input_dtype(input_param_name='x')