diff --git a/paddle/phi/kernels/funcs/compare_functors.h b/paddle/phi/kernels/funcs/compare_functors.h
index 569fed7b7fbab90e77c02beecbb18b486c801a4f..e16083506bbe054accad3a9b76ce533fb3d74ac9 100644
--- a/paddle/phi/kernels/funcs/compare_functors.h
+++ b/paddle/phi/kernels/funcs/compare_functors.h
@@ -13,6 +13,7 @@
 // limitations under the License.
 
 #pragma once
+#include <math.h>
 
 namespace phi {
 namespace funcs {
@@ -35,6 +36,10 @@ template <typename InT, typename OutT = bool>
 struct EqualFunctor {
   HOSTDEVICE OutT operator()(const InT a, const InT b) const {
     if (std::is_floating_point<InT>::value) {
+      if (isinf(static_cast<float>(a)) || isinf(static_cast<float>(b)))
+        return static_cast<OutT>(a == b);
+      if (isnan(static_cast<float>(a)) || isnan(static_cast<float>(b)))
+        return static_cast<OutT>(false);
       return static_cast<OutT>(fabs(static_cast<double>(a - b)) < 1e-8);
     } else {
       return static_cast<OutT>(a == b);
diff --git a/python/paddle/fluid/tests/unittests/test_compare_op.py b/python/paddle/fluid/tests/unittests/test_compare_op.py
index f1bacfbb6f8f8a203ec0295ffd6a5ea43ffd7522..731eedfca60a08bdedff5192d2703d4b3a0e371d 100755
--- a/python/paddle/fluid/tests/unittests/test_compare_op.py
+++ b/python/paddle/fluid/tests/unittests/test_compare_op.py
@@ -150,6 +150,102 @@ def create_paddle_case(op_type, callback):
                 self.assertEqual((out.numpy() == self.real_result).all(), True)
                 paddle.enable_static()
 
+        def test_dynamic_api_inf_1(self):
+            if self.op_type == "equal":
+                paddle.disable_static()
+                x1 = np.array([1, float('inf'), float('inf')]).astype(np.int64)
+                x = paddle.to_tensor(x1)
+                y1 = np.array([1, float('-inf'), float('inf')]).astype(np.int64)
+                y = paddle.to_tensor(y1)
+                op = eval("paddle.%s" % (self.op_type))
+                out = op(x, y)
+                self.real_result = (x1 == y1).astype(np.int64)
+                self.assertEqual(
+                    (out.numpy().astype(np.int64) == self.real_result).all(),
+                    True)
+                paddle.enable_static()
+
+        def test_dynamic_api_inf_2(self):
+            if self.op_type == "equal":
+                paddle.disable_static()
+                x1 = np.array([1, float('inf'),
+                               float('inf')]).astype(np.float32)
+                x = paddle.to_tensor(x1)
+                y1 = np.array([1, float('-inf'),
+                               float('inf')]).astype(np.float32)
+                y = paddle.to_tensor(y1)
+                op = eval("paddle.%s" % (self.op_type))
+                out = op(x, y)
+                self.real_result = (x1 == y1).astype(np.int64)
+                self.assertEqual(
+                    (out.numpy().astype(np.int64) == self.real_result).all(),
+                    True)
+                paddle.enable_static()
+
+        def test_dynamic_api_inf_3(self):
+            if self.op_type == "equal":
+                paddle.disable_static()
+                x1 = np.array([1, float('inf'),
+                               float('-inf')]).astype(np.float32)
+                x = paddle.to_tensor(x1)
+                y1 = np.array([1, 2, 3]).astype(np.float32)
+                y = paddle.to_tensor(y1)
+                op = eval("paddle.%s" % (self.op_type))
+                out = op(x, y)
+                self.real_result = (x1 == y1).astype(np.int64)
+                self.assertEqual(
+                    (out.numpy().astype(np.int64) == self.real_result).all(),
+                    True)
+                paddle.enable_static()
+
+        def test_dynamic_api_nan_1(self):
+            if self.op_type == "equal":
+                paddle.disable_static()
+                x1 = np.array([1, float('nan'), float('nan')]).astype(np.int64)
+                x = paddle.to_tensor(x1)
+                y1 = np.array([1, float('-nan'), float('nan')]).astype(np.int64)
+                y = paddle.to_tensor(y1)
+                op = eval("paddle.%s" % (self.op_type))
+                out = op(x, y)
+                self.real_result = (x1 == y1).astype(np.int64)
+                self.assertEqual(
+                    (out.numpy().astype(np.int64) == self.real_result).all(),
+                    True)
+                paddle.enable_static()
+
+        def test_dynamic_api_nan_2(self):
+            if self.op_type == "equal":
+                paddle.disable_static()
+                x1 = np.array([1, float('nan'),
+                               float('nan')]).astype(np.float32)
+                x = paddle.to_tensor(x1)
+                y1 = np.array([1, float('-nan'),
+                               float('nan')]).astype(np.float32)
+                y = paddle.to_tensor(y1)
+                op = eval("paddle.%s" % (self.op_type))
+                out = op(x, y)
+                self.real_result = (x1 == y1).astype(np.int64)
+                self.assertEqual(
+                    (out.numpy().astype(np.int64) == self.real_result).all(),
+                    True)
+                paddle.enable_static()
+
+        def test_dynamic_api_nan_3(self):
+            if self.op_type == "equal":
+                paddle.disable_static()
+                x1 = np.array([1, float('-nan'),
+                               float('nan')]).astype(np.float32)
+                x = paddle.to_tensor(x1)
+                y1 = np.array([1, 2, 1]).astype(np.float32)
+                y = paddle.to_tensor(y1)
+                op = eval("paddle.%s" % (self.op_type))
+                out = op(x, y)
+                self.real_result = (x1 == y1).astype(np.int64)
+                self.assertEqual(
+                    (out.numpy().astype(np.int64) == self.real_result).all(),
+                    True)
+                paddle.enable_static()
+
         def test_not_equal(self):
             if self.op_type == "not_equal":
                 paddle.disable_static()