diff --git a/Lib/imaplib.py b/Lib/imaplib.py
index 357ba83891d..f66a83bae2a 100644
--- a/Lib/imaplib.py
+++ b/Lib/imaplib.py
@@ -22,7 +22,7 @@ Public functions:       Internaldate2tuple
 
 __version__ = "2.58"
 
-import binascii, random, re, socket, subprocess, sys, time
+import binascii, errno, random, re, socket, subprocess, sys, time
 
 __all__ = ["IMAP4", "IMAP4_stream", "Internaldate2tuple",
            "Int2AP", "ParseFlags", "Time2Internaldate"]
@@ -248,8 +248,14 @@ class IMAP4:
     def shutdown(self):
         """Close I/O established in "open"."""
         self.file.close()
-        self.sock.shutdown(socket.SHUT_RDWR)
-        self.sock.close()
+        try:
+            self.sock.shutdown(socket.SHUT_RDWR)
+        except socket.error as e:
+            # The server might already have closed the connection
+            if e.errno != errno.ENOTCONN:
+                raise
+        finally:
+            self.sock.close()
 
 
     def socket(self):