diff --git a/Lib/multiprocessing/connection.py b/Lib/multiprocessing/connection.py
index 530a8dfe4e5..a02793ff26b 100644
--- a/Lib/multiprocessing/connection.py
+++ b/Lib/multiprocessing/connection.py
@@ -348,7 +348,10 @@ if sys.platform == 'win32':
             try:
                 win32.ConnectNamedPipe(handle, win32.NULL)
             except WindowsError, e:
-                if e.args[0] != win32.ERROR_PIPE_CONNECTED:
+                # ERROR_NO_DATA can occur if a client has already connected,
+                # written data and then disconnected -- see Issue 14725.
+                if e.args[0] not in (win32.ERROR_PIPE_CONNECTED,
+                                     win32.ERROR_NO_DATA):
                     raise
             return _multiprocessing.PipeConnection(handle)
 
diff --git a/Lib/test/test_multiprocessing.py b/Lib/test/test_multiprocessing.py
index eeb768f7d7a..0fe649799a3 100644
--- a/Lib/test/test_multiprocessing.py
+++ b/Lib/test/test_multiprocessing.py
@@ -1669,6 +1669,23 @@ class _TestListenerClient(BaseTestCase):
             self.assertEqual(conn.recv(), 'hello')
             p.join()
             l.close()
+
+    def test_issue14725(self):
+        l = self.connection.Listener()
+        p = self.Process(target=self._test, args=(l.address,))
+        p.daemon = True
+        p.start()
+        time.sleep(1)
+        # On Windows the client process should by now have connected,
+        # written data and closed the pipe handle by now.  This causes
+        # ConnectNamdedPipe() to fail with ERROR_NO_DATA.  See Issue
+        # 14725.
+        conn = l.accept()
+        self.assertEqual(conn.recv(), 'hello')
+        conn.close()
+        p.join()
+        l.close()
+
 #
 # Test of sending connection and socket objects between processes
 #
diff --git a/Modules/_multiprocessing/win32_functions.c b/Modules/_multiprocessing/win32_functions.c
index 1666aa9132f..9425929469e 100644
--- a/Modules/_multiprocessing/win32_functions.c
+++ b/Modules/_multiprocessing/win32_functions.c
@@ -244,6 +244,7 @@ create_win32_namespace(void)
     Py_INCREF(&Win32Type);
 
     WIN32_CONSTANT(F_DWORD, ERROR_ALREADY_EXISTS);
+    WIN32_CONSTANT(F_DWORD, ERROR_NO_DATA);
     WIN32_CONSTANT(F_DWORD, ERROR_PIPE_BUSY);
     WIN32_CONSTANT(F_DWORD, ERROR_PIPE_CONNECTED);
     WIN32_CONSTANT(F_DWORD, ERROR_SEM_TIMEOUT);