diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 54910cd8054a1f..31ebcb3b8b0b00 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -14,6 +14,15 @@
 from fractions import Fraction
 from collections import abc, Counter
 
+
+class MyIndex:
+    def __init__(self, value):
+        self.value = value
+
+    def __index__(self):
+        return self.value
+
+
 class TestBasicOps:
     # Superclass with tests common to all generators.
     # Subclasses must arrange for self.gen to retrieve the Random instance
@@ -809,6 +818,9 @@ def test_getrandbits(self):
         self.gen.seed(1234567)
         self.assertEqual(self.gen.getrandbits(100),
                          97904845777343510404718956115)
+        self.gen.seed(1234567)
+        self.assertEqual(self.gen.getrandbits(MyIndex(100)),
+                         97904845777343510404718956115)
 
     def test_getrandbits_2G_bits(self):
         size = 2**31