diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 45997cb..87b298e 100644
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1065,7 +1065,8 @@
         self.closed = False
         self.members = []       # list of members as TarInfo objects
         self._loaded = False    # flag if all members have been read
-        self.offset = 0L        # current position in the archive file
+        self.offset = self.fileobj.tell()
+                                # current position in the archive file
         self.inodes = {}        # dictionary caching the inodes of
                                 # archive members already added