diff --git a/Lib/tarfile.py b/Lib/tarfile.py
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1718,13 +1718,15 @@
         except (ImportError, AttributeError):
             raise CompressionError("gzip module is not available")
 
-        if fileobj is None:
-            fileobj = bltn_open(name, mode + "b")
+        try:
+            fileobj = gzip.GzipFile(name, mode + "b", compresslevel, fileobj)
+        except OSError:
+            if fileobj is not None and mode == 'r':
+                raise ReadError("not a gzip file")
+            raise
 
         try:
-            t = cls.taropen(name, mode,
-                gzip.GzipFile(name, mode, compresslevel, fileobj),
-                **kwargs)
+            t = cls.taropen(name, mode, fileobj, **kwargs)
         except IOError:
             if mode == 'r':
                 raise ReadError("not a gzip file")