diff --git a/django/core/mail/backends/smtp.py b/django/core/mail/backends/smtp.py
index baffa8f2df..3ae08f4340 100644
--- a/django/core/mail/backends/smtp.py
+++ b/django/core/mail/backends/smtp.py
@@ -60,6 +60,8 @@ class EmailBackend(BaseEmailBackend):
 
     def close(self):
         """Closes the connection to the email server."""
+        if self.connection is None:
+            return
         try:
             try:
                 self.connection.quit()
diff --git a/tests/regressiontests/mail/tests.py b/tests/regressiontests/mail/tests.py
index 9ab8c2c301..059dd6d09a 100644
--- a/tests/regressiontests/mail/tests.py
+++ b/tests/regressiontests/mail/tests.py
@@ -492,6 +492,16 @@ class BaseEmailBackendTests(object):
         self.assertEqual(message.get('from'), "tester")
         self.assertEqual(message.get('to'), "django")
 
+    def test_close_connection(self):
+        """
+        Test that connection can be closed (even when not explicitely opened)
+        """
+        conn = mail.get_connection(username='', password='')
+        try:
+            conn.close()
+        except Exception as e:
+            self.fail("close() unexpectedly raised an exception: %s" % e)
+
 
 class LocmemBackendTests(BaseEmailBackendTests, TestCase):
     email_backend = 'django.core.mail.backends.locmem.EmailBackend'