diff -r ec12fbf449a5 Lib/socketserver.py
--- a/Lib/socketserver.py	Mon Feb 08 17:57:22 2016 +0200
+++ b/Lib/socketserver.py	Tue Feb 09 22:34:51 2016 +0200
@@ -319,6 +319,8 @@
             except:
                 self.handle_error(request, client_address)
                 self.shutdown_request(request)
+        else:
+            self.shutdown_request(request)
 
     def handle_timeout(self):
         """Called if no new request arrives within self.timeout.
diff -r ec12fbf449a5 Lib/test/test_socketserver.py
--- a/Lib/test/test_socketserver.py	Mon Feb 08 17:57:22 2016 +0200
+++ b/Lib/test/test_socketserver.py	Tue Feb 09 22:34:51 2016 +0200
@@ -280,6 +280,25 @@
                 socketserver.TCPServer((HOST, -1),
                                        socketserver.StreamRequestHandler)
 
+    def test_shutdown_request_if_verify_false(self):
+        # Issue #26309: BaseServer should call shutdown_request even if
+        # verify_request is False
+        class MyServer(socketserver.TCPServer):
+            def verify_request(self, request, client_address):
+                return False
+
+            def process_request(self, request, client_address):
+                socketserver.TCPServer.shutdown_request(self, request)
+
+            def shutdown_request(self, request):
+                # we pass None as client_address because we don't have it and it's okay because it's not used
+                self.finish_request(request, None)
+                self.close_request(request)
+
+        self.run_server(MyServer,
+                        socketserver.StreamRequestHandler,
+                        self.stream_examine)
+
 
 class MiscTestCase(unittest.TestCase):