diff --git a/paddle/fluid/operators/fill_constant_op.h b/paddle/fluid/operators/fill_constant_op.h
index 41fcf3750878e61616caff84c4f44d18d1d36815..239083f88d9c63c4790fe4dd3060a5cf473ff73c 100644
--- a/paddle/fluid/operators/fill_constant_op.h
+++ b/paddle/fluid/operators/fill_constant_op.h
@@ -14,9 +14,11 @@ limitations under the License. */
 
 #pragma once
 
+#include <limits>
 #include <sstream>
 #include <string>
 #include <vector>
+
 #include "paddle/fluid/framework/data_type.h"
 #include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/operators/math/math_function.h"
@@ -45,15 +47,22 @@ class FillConstantKernel : public framework::OpKernel<T> {
     if (str_value.empty()) {
       value = static_cast<T>(float_value);
     } else {
-      std::stringstream convert_stream(str_value);
-      if (std::is_same<int64_t, T>::value) {
-        int64_t tmp_value;
-        convert_stream >> tmp_value;
-        value = static_cast<T>(tmp_value);
+      // handle NaN/Inf first, which cannot be read from stream.
+      if (str_value == "inf") {
+        value = static_cast<T>(std::numeric_limits<double>::infinity());
+      } else if (str_value == "nan") {
+        value = static_cast<T>(std::numeric_limits<double>::quiet_NaN());
       } else {
-        double tmp_value;
-        convert_stream >> tmp_value;
-        value = static_cast<T>(tmp_value);
+        std::stringstream convert_stream(str_value);
+        if (std::is_same<int64_t, T>::value) {
+          int64_t tmp_value;
+          convert_stream >> tmp_value;
+          value = static_cast<T>(tmp_value);
+        } else {
+          double tmp_value;
+          convert_stream >> tmp_value;
+          value = static_cast<T>(tmp_value);
+        }
       }
     }
     if (ctx.HasInput("ValueTensor")) {
diff --git a/python/paddle/fluid/tests/unittests/test_fill_constant_op.py b/python/paddle/fluid/tests/unittests/test_fill_constant_op.py
index 43069470680c7d49071ce54bf3649962c56f06ea..babfcdb9040df78f13204bbcad28ca01cff48040 100644
--- a/python/paddle/fluid/tests/unittests/test_fill_constant_op.py
+++ b/python/paddle/fluid/tests/unittests/test_fill_constant_op.py
@@ -330,6 +330,16 @@ class TestFillConstantImperative(unittest.TestCase):
                 res4.numpy(), np.full(
                     [1, 2], 88, dtype="int32"))
 
+    def test_nan(self):
+        with fluid.dygraph.guard():
+            res = fluid.layers.fill_constant([1], 'float32', np.nan)
+            self.assertTrue(np.isnan(res.numpy().item(0)))
+
+    def test_inf(self):
+        with fluid.dygraph.guard():
+            res = fluid.layers.fill_constant([1], 'float32', np.inf)
+            self.assertTrue(np.isinf(res.numpy().item(0)))
+
 
 class TestFillConstantOpError(unittest.TestCase):
     def test_errors(self):