diff --git a/Lib/mailbox.py b/Lib/mailbox.py
--- a/Lib/mailbox.py
+++ b/Lib/mailbox.py
@@ -1919,9 +1919,9 @@
 
     def close(self):
         """Close the file."""
-        if hasattr(self._file, 'close'):
+        if hasattr(self, '_file'):
             self._file.close()
-        del self._file
+            del self._file
 
     def _read(self, size, read_method):
         """Read size bytes using read_method."""
@@ -1953,7 +1953,7 @@
 
     @property
     def closed(self):
-        return self._file.closed
+        return not hasattr(self, '_file')
 
 
 class _PartialFile(_ProxyFile):
@@ -1991,7 +1991,8 @@
     def close(self):
         # do *not* close the underlying file object for partial files,
         # since it's global to the mailbox object
-        del self._file
+        if hasattr(self, '_file'):
+            del self._file
 
 
 def _lock_file(f, dotlock=True):
diff --git a/Lib/test/test_mailbox.py b/Lib/test/test_mailbox.py
--- a/Lib/test/test_mailbox.py
+++ b/Lib/test/test_mailbox.py
@@ -1834,9 +1834,13 @@
 
     def _test_close(self, proxy):
         # Close a file
+        self.assertFalse(proxy.closed)
         proxy.close()
-        self.assertRaises(AttributeError, lambda: proxy.close())
-
+        self.assertTrue(proxy.closed)
+        try:
+            proxy.close()
+        except:
+            self.fail('Proxy.close() failure')
 
 class TestProxyFile(TestProxyFileBase):