diff --git a/paddle/fluid/operators/elementwise/elementwise_max_op.cc b/paddle/fluid/operators/elementwise/elementwise_max_op.cc
index cc27bab72005752af372ee1a273258033e028c18..91da732ef0d3dfbda5d9b7734071ec5831bcfa3f 100644
--- a/paddle/fluid/operators/elementwise/elementwise_max_op.cc
+++ b/paddle/fluid/operators/elementwise/elementwise_max_op.cc
@@ -124,13 +124,17 @@ REGISTER_OP_CPU_KERNEL(
     ops::ElementwiseMaxKernel<paddle::platform::CPUDeviceContext, float>,
     ops::ElementwiseMaxKernel<paddle::platform::CPUDeviceContext, double>,
     ops::ElementwiseMaxKernel<paddle::platform::CPUDeviceContext, int>,
-    ops::ElementwiseMaxKernel<paddle::platform::CPUDeviceContext, int64_t>);
+    ops::ElementwiseMaxKernel<paddle::platform::CPUDeviceContext, int64_t>,
+    ops::ElementwiseMaxKernel<paddle::platform::CPUDeviceContext,
+                              paddle::platform::bfloat16>);
 REGISTER_OP_CPU_KERNEL(
     elementwise_max_grad,
     ops::ElementwiseMaxGradKernel<paddle::platform::CPUDeviceContext, float>,
     ops::ElementwiseMaxGradKernel<paddle::platform::CPUDeviceContext, double>,
     ops::ElementwiseMaxGradKernel<paddle::platform::CPUDeviceContext, int>,
-    ops::ElementwiseMaxGradKernel<paddle::platform::CPUDeviceContext, int64_t>);
+    ops::ElementwiseMaxGradKernel<paddle::platform::CPUDeviceContext, int64_t>,
+    ops::ElementwiseMaxGradKernel<paddle::platform::CPUDeviceContext,
+                                  paddle::platform::bfloat16>);
 
 REGISTER_OP_VERSION(elementwise_max)
     .AddCheckpoint(
diff --git a/paddle/fluid/operators/elementwise/elementwise_max_op.cu b/paddle/fluid/operators/elementwise/elementwise_max_op.cu
index 7433c505f472a28c7be118856ee8fa410025449a..123332a4a23de5c9534c8523993b87d8738f9869 100644
--- a/paddle/fluid/operators/elementwise/elementwise_max_op.cu
+++ b/paddle/fluid/operators/elementwise/elementwise_max_op.cu
@@ -69,6 +69,8 @@ REGISTER_OP_CUDA_KERNEL(
     elementwise_max,
     ops::ElementwiseMaxKernel<paddle::platform::CUDADeviceContext,
                               paddle::platform::float16>,
+    ops::ElementwiseMaxKernel<paddle::platform::CUDADeviceContext,
+                              paddle::platform::bfloat16>,
     ops::ElementwiseMaxKernel<paddle::platform::CUDADeviceContext, float>,
     ops::ElementwiseMaxKernel<paddle::platform::CUDADeviceContext, double>,
     ops::ElementwiseMaxKernel<paddle::platform::CUDADeviceContext, int>,
@@ -77,6 +79,8 @@ REGISTER_OP_CUDA_KERNEL(
     elementwise_max_grad,
     ops::ElementwiseMaxGradKernel<paddle::platform::CUDADeviceContext,
                                   paddle::platform::float16>,
+    ops::ElementwiseMaxGradKernel<paddle::platform::CUDADeviceContext,
+                                  paddle::platform::bfloat16>,
     ops::ElementwiseMaxGradKernel<paddle::platform::CUDADeviceContext, float>,
     ops::ElementwiseMaxGradKernel<paddle::platform::CUDADeviceContext, double>,
     ops::ElementwiseMaxGradKernel<paddle::platform::CUDADeviceContext, int>,
diff --git a/python/paddle/fluid/tests/unittests/op_test.py b/python/paddle/fluid/tests/unittests/op_test.py
index 85423df3d382831738c2c64ea845d0661f9cdbb7..ec3b68086b06593b035b60825a52b0ec32b8281d 100644
--- a/python/paddle/fluid/tests/unittests/op_test.py
+++ b/python/paddle/fluid/tests/unittests/op_test.py
@@ -168,8 +168,10 @@ def get_numeric_gradient(place,
         elif tensor_to_check._dtype() == core.VarDesc.VarType.BF16:
             numpy_tensor = np.array(tensor).astype(np.uint16)
             numpy_tensor = numpy_tensor.flatten()
-            return struct.unpack('<f', struct.pack('<I', numpy_tensor[i]
-                                                   << 16))[0]
+            return struct.unpack('<f',
+                                 struct.pack('<I',
+                                             np.uint32(numpy_tensor[i])
+                                             << np.uint32(16)))[0]
         elif tensor_to_check_dtype == np.float32:
             return tensor._get_float_element(i)
         elif tensor_to_check_dtype == np.float64:
@@ -272,7 +274,7 @@ def convert_float_to_uint16(float_list, data_format="NCHW"):
 def convert_uint16_to_float(in_list):
     in_list = np.asarray(in_list)
     out = np.vectorize(
-        lambda x: struct.unpack('<f', struct.pack('<I', x << 16))[0],
+        lambda x: struct.unpack('<f', struct.pack('<I', np.uint32(x) << np.uint32(16)))[0],
         otypes=[np.float32])(in_list.flat)
     return np.reshape(out, in_list.shape)
 
diff --git a/python/paddle/fluid/tests/unittests/test_elementwise_max_op.py b/python/paddle/fluid/tests/unittests/test_elementwise_max_op.py
index 624619f499f6664d4dfd0fd56a3b547a78c586a9..719ee5df6dbbf5e766986c462cb772519ad28613 100644
--- a/python/paddle/fluid/tests/unittests/test_elementwise_max_op.py
+++ b/python/paddle/fluid/tests/unittests/test_elementwise_max_op.py
@@ -16,7 +16,10 @@ from __future__ import print_function
 
 import unittest
 import numpy as np
-from op_test import OpTest, skip_check_grad_ci
+from op_test import OpTest, skip_check_grad_ci, convert_float_to_uint16
+import os
+import re
+import paddle.fluid.core as core
 
 
 class TestElementwiseOp(OpTest):
@@ -46,6 +49,38 @@ class TestElementwiseOp(OpTest):
             ['X'], 'Out', max_relative_error=0.005, no_grad_set=set('Y'))
 
 
+@unittest.skipIf(
+    core.is_compiled_with_cuda() and core.cudnn_version() < 8100,
+    "run test when gpu is availble and the minimum cudnn version is 8.1.0.")
+class TestElementwiseBF16Op(OpTest):
+    def setUp(self):
+        self.op_type = "elementwise_max"
+        self.dtype = np.uint16
+        # If x and y have the same value, the max() is not differentiable.
+        # So we generate test data by the following method
+        # to avoid them being too close to each other.
+        x = np.random.uniform(0.1, 1, [13, 17]).astype(np.float32)
+        sgn = np.random.choice([-1, 1], [13, 17]).astype(np.float32)
+        y = x + sgn * np.random.uniform(0.1, 1, [13, 17]).astype(np.float32)
+        self.inputs = {
+            'X': convert_float_to_uint16(x),
+            'Y': convert_float_to_uint16(y)
+        }
+        self.outputs = {'Out': convert_float_to_uint16(np.maximum(x, y))}
+
+    def test_check_output(self):
+        self.check_output()
+
+    def test_check_grad_normal(self):
+        self.check_grad(['X', 'Y'], 'Out')
+
+    def test_check_grad_ingore_x(self):
+        self.check_grad(['Y'], 'Out', no_grad_set=set("X"))
+
+    def test_check_grad_ingore_y(self):
+        self.check_grad(['X'], 'Out', no_grad_set=set('Y'))
+
+
 @skip_check_grad_ci(
     reason="[skip shape check] Use y_shape(1) to test broadcast.")
 class TestElementwiseMaxOp_scalar(TestElementwiseOp):