diff --git a/django/core/mail/backends/smtp.py b/django/core/mail/backends/smtp.py
index b6f7f560ed6..baffa8f2dfb 100644
--- a/django/core/mail/backends/smtp.py
+++ b/django/core/mail/backends/smtp.py
@@ -63,9 +63,10 @@ class EmailBackend(BaseEmailBackend):
         try:
             try:
                 self.connection.quit()
-            except socket.sslerror:
+            except (socket.sslerror, smtplib.SMTPServerDisconnected):
                 # This happens when calling quit() on a TLS connection
-                # sometimes.
+                # sometimes, or when the connection was already disconnected
+                # by the server.
                 self.connection.close()
             except:
                 if self.fail_silently:
diff --git a/tests/regressiontests/mail/tests.py b/tests/regressiontests/mail/tests.py
index a8fbf20fd60..9ab8c2c301f 100644
--- a/tests/regressiontests/mail/tests.py
+++ b/tests/regressiontests/mail/tests.py
@@ -659,9 +659,9 @@ class FakeSMTPServer(smtpd.SMTPServer, threading.Thread):
         asyncore.close_all()
 
     def stop(self):
-        assert self.active
-        self.active = False
-        self.join()
+        if self.active:
+            self.active = False
+            self.join()
 
 
 class SMTPBackendTests(BaseEmailBackendTests, TestCase):
@@ -715,3 +715,16 @@ class SMTPBackendTests(BaseEmailBackendTests, TestCase):
         backend = smtp.EmailBackend(username='', password='')
         self.assertEqual(backend.username, '')
         self.assertEqual(backend.password, '')
+
+    def test_server_stopped(self):
+        """
+        Test that closing the backend while the SMTP server is stopped doesn't
+        raise an exception.
+        """
+        backend = smtp.EmailBackend(username='', password='')
+        backend.open()
+        self.server.stop()
+        try:
+            backend.close()
+        except Exception as e:
+            self.fail("close() unexpectedly raised an exception: %s" % e)