diff --git a/Lib/calendar.py b/Lib/calendar.py
index 0301d6b5d6c..3bbf399649f 100644
--- a/Lib/calendar.py
+++ b/Lib/calendar.py
@@ -161,7 +161,11 @@ class Calendar(object):
         oneday = datetime.timedelta(days=1)
         while True:
             yield date
-            date += oneday
+            try:
+                date += oneday
+            except OverflowError:
+                # Adding one day could fail after datetime.MAXYEAR
+                break
             if date.month != month and date.weekday() == self.firstweekday:
                 break
 
diff --git a/Lib/test/test_calendar.py b/Lib/test/test_calendar.py
index e0f63997d5f..e594e01be0e 100644
--- a/Lib/test/test_calendar.py
+++ b/Lib/test/test_calendar.py
@@ -6,6 +6,7 @@ from test.script_helper import assert_python_ok
 import time
 import locale
 import sys
+import datetime
 
 result_2004_01_text = """
     January 2004
@@ -464,6 +465,11 @@ class CalendarTestCase(unittest.TestCase):
         new_october = calendar.TextCalendar().formatmonthname(2010, 10, 10)
         self.assertEqual(old_october, new_october)
 
+    def test_itermonthdates(self):
+        # ensure itermonthdates doesn't overflow after datetime.MAXYEAR
+        # see #15421
+        list(calendar.Calendar().itermonthdates(datetime.MAXYEAR, 12))
+
 
 class MonthCalendarTestCase(unittest.TestCase):
     def setUp(self):
diff --git a/Misc/NEWS b/Misc/NEWS
index 5d6ca0f923e..abe8eb8028f 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -36,6 +36,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #15421: fix an OverflowError in Calendar.itermonthdates() after
+  datetime.MAXYEAR.  Patch by Cédric Krier.
+
 - Issue #15970: xml.etree.ElementTree now serializes correctly the empty HTML
   elements 'meta' and 'param'.