diff --git a/tensorflow/core/ops/math_ops.cc b/tensorflow/core/ops/math_ops.cc
index 3eff728f032..a9e5e7824d2 100644
--- a/tensorflow/core/ops/math_ops.cc
+++ b/tensorflow/core/ops/math_ops.cc
@@ -1437,7 +1437,24 @@ REGISTER_OP("Bincount")
     .Attr("T: {int32, int64, float32, float64}")
     .Output("bins: T")
     .SetShapeFn([](InferenceContext* c) {
-      c->set_output(0, c->UnknownShapeOfRank(1));
+      ShapeHandle unused;
+      // The input `size` must be a scalar.
+      TF_RETURN_IF_ERROR(c->WithRank(c->input(1), 0, &unused));
+
+      const Tensor* size_tensor = c->input_tensor(1);
+      if (size_tensor == nullptr) {
+        // Return unknown shape if size is not known.
+        c->set_output(0, c->UnknownShapeOfRank(1));
+        return Status::OK();
+      }
+
+      // Return `[size]` shape if size is known.
+      int32 size_val = size_tensor->scalar<int32>()();
+      if (size_val < 0) {
+        return errors::InvalidArgument("size (", size_val,
+                                       ") must be non-negative");
+      }
+      c->set_output(0, c->MakeShape({size_val}));
       return Status::OK();
     });
 
diff --git a/tensorflow/core/ops/math_ops_test.cc b/tensorflow/core/ops/math_ops_test.cc
index be4c3ed2b6e..05379a7d699 100644
--- a/tensorflow/core/ops/math_ops_test.cc
+++ b/tensorflow/core/ops/math_ops_test.cc
@@ -559,4 +559,16 @@ TEST(MathOpsTest, QuantizedAdd_ShapeFn) {
   INFER_ERROR("must be rank 0", op, "?;?;?;?;[3];?");
   INFER_ERROR("must be rank 0", op, "?;?;?;?;?;[4]");
 }
+
+TEST(MathOpsTest, Bincount_ShapeFn) {
+  ShapeInferenceTestOp op("Bincount");
+
+  // size should be scalar.
+  INFER_ERROR("Shape must be rank 0 but is rank 1", op, "?;[1];?");
+
+  INFER_OK(op, "?;?;?", "[?]");
+  INFER_OK(op, "?;[];?", "[?]");
+  INFER_OK(op, "[?];[];?", "[?]");
+  INFER_OK(op, "[?];[];[?]", "[?]");
+}
 }  // end namespace tensorflow
diff --git a/tensorflow/python/kernel_tests/bincount_op_test.py b/tensorflow/python/kernel_tests/bincount_op_test.py
index 8a58b3f97ec..8177cdd454e 100644
--- a/tensorflow/python/kernel_tests/bincount_op_test.py
+++ b/tensorflow/python/kernel_tests/bincount_op_test.py
@@ -22,6 +22,8 @@ import numpy as np
 from tensorflow.python.framework import dtypes
 from tensorflow.python.framework import errors
 from tensorflow.python.framework import test_util
+from tensorflow.python.ops import array_ops
+from tensorflow.python.ops import gen_math_ops
 from tensorflow.python.ops import math_ops
 from tensorflow.python.platform import googletest
 
@@ -97,6 +99,22 @@ class BincountTest(test_util.TensorFlowTestCase):
       with self.assertRaises(errors.InvalidArgumentError):
         math_ops.bincount([1, 2, 3, -1, 6, 8]).eval()
 
+  def test_shape_function(self):
+    # size must be scalar.
+    with self.assertRaisesRegexp(
+        ValueError, "Shape must be rank 0 but is rank 1 for 'Bincount'"):
+      gen_math_ops.bincount([1, 2, 3, -1, 6, 8], [1], [])
+    # size must be positive.
+    with self.assertRaisesRegexp(ValueError, "must be non-negative"):
+      gen_math_ops.bincount([1, 2, 3, -1, 6, 8], -5, [])
+    # if size is a constant then the shape is known.
+    v1 = gen_math_ops.bincount([1, 2, 3, -1, 6, 8], 5, [])
+    self.assertAllEqual(v1.get_shape().as_list(), [5])
+    # if size is a placeholder then the shape is unknown.
+    s = array_ops.placeholder(dtype=dtypes.int32)
+    v2 = gen_math_ops.bincount([1, 2, 3, -1, 6, 8], s, [])
+    self.assertAllEqual(v2.get_shape().as_list(), [None])
+
 
 if __name__ == "__main__":
   googletest.main()