diff -r 954b83e0c79a Lib/imghdr.py
--- a/Lib/imghdr.py	Tue Dec 17 12:45:44 2013 +0200
+++ b/Lib/imghdr.py	Tue Dec 17 13:12:25 2013 +0200
@@ -8,14 +8,16 @@
 
 def what(file, h=None):
     if h is None:
-        if isinstance(file, str):
+        try:
             f = open(file, 'rb')
-            h = f.read(32)
-        else:
+        except TypeError:
+            # a file stream
             location = file.tell()
             h = file.read(32)
             file.seek(location)
             f = None
+        else:
+            h = f.read(32)
     else:
         f = None
     try:
diff -r 954b83e0c79a Lib/test/test_imghdr.py
--- a/Lib/test/test_imghdr.py	Tue Dec 17 12:45:44 2013 +0200
+++ b/Lib/test/test_imghdr.py	Tue Dec 17 13:12:25 2013 +0200
@@ -1,4 +1,6 @@
 import unittest
+import os
+import io
 from test.support import TESTFN, unlink
 import imghdr
 
@@ -41,6 +43,18 @@
                 self.assertEqual(imghdr.what(TESTFN),
                                  format)
 
+    def test_file_argument(self):
+        with open(TESTFN, 'wb') as stream:
+            stream.write(b'eggs')
+        # will be closed by `imghdr.what`          
+        stream = open(TESTFN, 'rb')
+        fileno = stream.fileno()
+        self.assertIsNone(imghdr.what(fileno))
+        self.assertIsNone(imghdr.what(TESTFN))
+        self.assertIsNone(imghdr.what(os.fsencode(TESTFN)))
+        with io.BytesIO(b'BMP') as stream:
+            self.assertEqual(imghdr.what(stream), 'bmp')
+
     def test_register_test(self):
         def test_jumbo(h, file):
             if h.startswith(b'eggs'):