diff --git a/Doc/library/math.rst b/Doc/library/math.rst
index ff937d27c6c..bfce41a7f4c 100644
--- a/Doc/library/math.rst
+++ b/Doc/library/math.rst
@@ -71,6 +71,9 @@ Number-theoretic and representation functions
    Return *x* factorial as an integer.  Raises :exc:`ValueError` if *x* is not integral or
    is negative.
 
+   .. deprecated:: 3.9
+      Accepting floats with integral values (like ``5.0``) is deprecated.
+
 
 .. function:: floor(x)
 
diff --git a/Doc/whatsnew/3.9.rst b/Doc/whatsnew/3.9.rst
index 62b013f7721..c5cb626a1b6 100644
--- a/Doc/whatsnew/3.9.rst
+++ b/Doc/whatsnew/3.9.rst
@@ -109,6 +109,11 @@ Build and C API Changes
 Deprecated
 ==========
 
+* Currently :func:`math.factorial` accepts :class:`float` instances with
+  non-negative integer values (like ``5.0``).  It raises a :exc:`ValueError`
+  for non-integral and negative floats.  It is deprecated now.  In future
+  Python versions it will raise a :exc:`TypeError` for all floats.
+  (Contributed by Serhiy Storchaka in :issue:`37315`.)
 
 
 Removed
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index adefa07a404..f25913941b8 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -501,21 +501,25 @@ class MathTests(unittest.TestCase):
 
     def testFactorial(self):
         self.assertEqual(math.factorial(0), 1)
-        self.assertEqual(math.factorial(0.0), 1)
         total = 1
         for i in range(1, 1000):
             total *= i
             self.assertEqual(math.factorial(i), total)
-            self.assertEqual(math.factorial(float(i)), total)
             self.assertEqual(math.factorial(i), py_factorial(i))
         self.assertRaises(ValueError, math.factorial, -1)
-        self.assertRaises(ValueError, math.factorial, -1.0)
         self.assertRaises(ValueError, math.factorial, -10**100)
-        self.assertRaises(ValueError, math.factorial, -1e100)
-        self.assertRaises(ValueError, math.factorial, math.pi)
 
     def testFactorialNonIntegers(self):
-        self.assertRaises(TypeError, math.factorial, decimal.Decimal(5.2))
+        with self.assertWarns(DeprecationWarning):
+            self.assertEqual(math.factorial(5.0), 120)
+        with self.assertWarns(DeprecationWarning):
+            self.assertRaises(ValueError, math.factorial, 5.2)
+        with self.assertWarns(DeprecationWarning):
+            self.assertRaises(ValueError, math.factorial, -1.0)
+        with self.assertWarns(DeprecationWarning):
+            self.assertRaises(ValueError, math.factorial, -1e100)
+        self.assertRaises(TypeError, math.factorial, decimal.Decimal('5'))
+        self.assertRaises(TypeError, math.factorial, decimal.Decimal('5.2'))
         self.assertRaises(TypeError, math.factorial, "5")
 
     # Other implementations may place different upper bounds.
@@ -524,7 +528,8 @@ class MathTests(unittest.TestCase):
         # Currently raises ValueError for inputs that are too large
         # to fit into a C long.
         self.assertRaises(OverflowError, math.factorial, 10**100)
-        self.assertRaises(OverflowError, math.factorial, 1e100)
+        with self.assertWarns(DeprecationWarning):
+            self.assertRaises(OverflowError, math.factorial, 1e100)
 
     def testFloor(self):
         self.assertRaises(TypeError, math.floor)
diff --git a/Misc/NEWS.d/next/Library/2019-06-17-11-59-52.bpo-37315.o1xFC0.rst b/Misc/NEWS.d/next/Library/2019-06-17-11-59-52.bpo-37315.o1xFC0.rst
new file mode 100644
index 00000000000..fd5981989b7
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-06-17-11-59-52.bpo-37315.o1xFC0.rst
@@ -0,0 +1,2 @@
+Deprecated accepting floats with integral value (like ``5.0``) in
+:func:`math.factorial`.
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 82a9a14724f..a75a3c929e7 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -1981,6 +1981,12 @@ math_factorial(PyObject *module, PyObject *arg)
     PyObject *result, *odd_part, *pyint_form;
 
     if (PyFloat_Check(arg)) {
+        if (PyErr_WarnEx(PyExc_DeprecationWarning,
+                         "Using factorial() with floats is deprecated",
+                         1) < 0)
+        {
+            return NULL;
+        }
         PyObject *lx;
         double dx = PyFloat_AS_DOUBLE((PyFloatObject *)arg);
         if (!(Py_IS_FINITE(dx) && dx == floor(dx))) {