diff --git a/Lib/gzip.py b/Lib/gzip.py
index 66fc88d..ef6befc 100644
--- a/Lib/gzip.py
+++ b/Lib/gzip.py
@@ -348,6 +348,15 @@
         elif isize != (self.size & 0xffffffff):
             raise IOError("Incorrect length of data produced")
 
+        # Gzip files can be padded with zeroes and still have archives.
+        # Consume all zero bytes and set the file position to the first
+        # non-zero byte. See http://www.gzip.org/#faq8
+        c = b"\x00"
+        while c == b"\x00":
+            c = self.fileobj.read(1)
+        if c:
+            self.fileobj.seek(-1, 1)
+
     @property
     def closed(self):
         return self.fileobj is None