diff --git a/Doc/library/os.rst b/Doc/library/os.rst
--- a/Doc/library/os.rst
+++ b/Doc/library/os.rst
@@ -1548,7 +1548,7 @@
       The *dir_fd* argument.
 
 
-.. function:: makedirs(path, mode=0o777, exist_ok=False)
+.. function:: makedirs(path, mode=0o777, exist_ok=False, on_wrong_mode=os.FAIL)
 
    .. index::
       single: directory; creating
@@ -1562,9 +1562,17 @@
 
    If *exists_ok* is ``False`` (the default), an :exc:`OSError` is raised if
    the target directory already exists.  If *exists_ok* is ``True`` an
-   :exc:`OSError` is still raised if the umask-masked *mode* is different from
-   the existing mode, on systems where the mode is used.  :exc:`OSError` will
-   also be raised if the directory creation fails.
+   :exc:`OSError` is still raised if *on_wrong_mode* is :data:`FAIL` (the
+   default) and the umask-masked *mode* is different from the existing mode, on
+   systems where the mode is used.  To avoid this, it's possible to either
+   supply :data:`IGNORE` or a callable for *on_wrong_mode*.  In the first case,
+   mode mismatches are simply ignored.  In the second case the callable is
+   invoked with the path of the directory in question and its conflicting mode.
+   It's up to the callable to decide whether this conflict is acceptable (do
+   nothing), fix it, or abort (raise an exception itself).  If the callable
+   returns, makedirs continues as if :data:`IGNORE` has been supplied.
+
+   :exc:`OSError` will also be raised if the directory creation fails.
 
    .. note::
 
@@ -1576,6 +1584,30 @@
    .. versionadded:: 3.2
       The *exist_ok* parameter.
 
+   .. versionadded:: 3.4
+      The *on_wrong_mode* parameter.
+
+
+.. data:: FAIL
+
+   If supplied as *on_wrong_mode* for :func:`makedirs` together with
+   *exist_ok=True*, calling it on an already existing directory with
+   a conflicting mode will raise a :exc:`OSError`.  This is the
+   default.
+
+   .. versionadded:: 3.4
+
+
+.. data:: IGNORE
+
+   If supplied as *on_wrong_mode* for :func:`makedirs` together with
+   ``exist_ok=True``, calling it on an already existing directory will succeed
+   regardless whether the actual mode of the directory conflicts with the
+   *mode* supplied.
+
+   .. versionadded:: 3.4
+
+
 
 .. function:: mkfifo(path, mode=0o666, *, dir_fd=None)
 
diff --git a/Lib/os.py b/Lib/os.py
--- a/Lib/os.py
+++ b/Lib/os.py
@@ -215,15 +215,27 @@
 # Super directory utilities.
 # (Inspired by Eric Raymond; the doc strings are mostly his)
 
-def makedirs(name, mode=0o777, exist_ok=False):
-    """makedirs(path [, mode=0o777][, exist_ok=False])
+FAIL = 0
+IGNORE = 1
+
+def makedirs(name, mode=0o777, exist_ok=False, on_wrong_mode=FAIL):
+    """makedirs(path [, mode=0o777][, exist_ok=False, [on_wrong_mode=FAIL]])
 
     Super-mkdir; create a leaf directory and all intermediate ones.
     Works like mkdir, except that any intermediate path segment (not
-    just the rightmost) will be created if it does not exist. If the
-    target directory with the same mode as we specified already exists,
-    raises an OSError if exist_ok is False, otherwise no exception is
-    raised.  This is recursive.
+    just the rightmost) will be created if it does not exist.
+
+    If the target directory already exists, the behavior of makedirs depends on
+    the mode of the directory and the values of exist_ok and on_wrong_mode:
+
+        - If exist_ok is False, FileExistsError is raised.
+        - If exist_ok is True and the mode matches, makedirs succeeds.
+        - If exist_ok is True and the mode doesn't match, on_wrong_mode
+          determines further action: os.FAIL (default) raises FileExistsError,
+          os.IGNORE succeeds.  If a callable is passed instead, it gets called
+          with the directory name in question and the mode of it as arguments.
+
+    This is recursive.
 
     """
     head, tail = path.split(name)
@@ -253,9 +265,18 @@
         if not (e.errno == errno.EEXIST and exist_ok and dir_exists and
                 actual_mode == expected_mode):
             if dir_exists and actual_mode != expected_mode:
-                e.strerror += ' (mode %o != expected mode %o)' % (
+                if on_wrong_mode == FAIL:
+                    e.strerror += ' (mode %o != expected mode %o)' % (
                         actual_mode, expected_mode)
-            raise
+                    raise
+                elif on_wrong_mode == IGNORE:
+                    pass
+                elif callable(on_wrong_mode):
+                    on_wrong_mode(name, actual_mode)
+                else:
+                    raise ValueError('Invalid value for on_wrong_mode.')
+            else:
+                raise
 
 def removedirs(name):
     """removedirs(path)
diff --git a/Lib/test/test_os.py b/Lib/test/test_os.py
--- a/Lib/test/test_os.py
+++ b/Lib/test/test_os.py
@@ -2,6 +2,9 @@
 # does add tests for a few functions which have been determined to be more
 # portable than they had been thought to be.
 
+from test import support
+from unittest import mock
+
 import os
 import errno
 import unittest
@@ -11,7 +14,6 @@
 import subprocess
 import time
 import shutil
-from test import support
 import contextlib
 import mmap
 import platform
@@ -894,6 +896,19 @@
         self.assertRaises(OSError, os.makedirs, path, exist_ok=True)
         os.remove(path)
 
+    def test_on_wrong_mode(self):
+        d = os.path.join(support.TESTFN, 'dir1')
+        os.makedirs(d, mode=0o333)
+        self.assertRaises(FileExistsError, os.makedirs, d, mode=0o777)
+        self.assertRaises(FileExistsError, os.makedirs, d, mode=0o777,
+                          exist_ok=True)
+        self.assertRaises(FileExistsError, os.makedirs, d, mode=0o777,
+                          exist_ok=True, on_wrong_mode=os.FAIL)
+        os.makedirs(d, mode=0o777, exist_ok=True, on_wrong_mode=os.IGNORE)
+        m = mock.MagicMock(name='on_wrong_mode')
+        os.makedirs(d, mode=0o777, exist_ok=True, on_wrong_mode=m)
+        m.assert_called_once_with(d, 0o311)
+
     def tearDown(self):
         path = os.path.join(support.TESTFN, 'dir1', 'dir2', 'dir3',
                             'dir4', 'dir5', 'dir6')