diff --git a/Lib/tarfile.py b/Lib/tarfile.py
index 40d438c45c4..ec8af064982 100755
--- a/Lib/tarfile.py
+++ b/Lib/tarfile.py
@@ -1618,7 +1618,7 @@ class TarFile(object):
             if not extfileobj and fileobj is not None:
                 fileobj.close()
             raise
-        t._extfileobj = extfileobj
+        t._extfileobj = False
         return t
 
     @classmethod
diff --git a/Lib/test/test_tarfile.py b/Lib/test/test_tarfile.py
index 72ae31addab..e0c91035bc0 100644
--- a/Lib/test/test_tarfile.py
+++ b/Lib/test/test_tarfile.py
@@ -857,6 +857,12 @@ class WriteTestBase(TarTest):
         tar.addfile(tarfile.TarInfo("foo"))
         tar.close()
         self.assertFalse(fobj.closed, "external fileobjs must never closed")
+        # Issue #20238: Incomplete gzip output with mode="w:gz"
+        data = fobj.getvalue()
+        del tar
+        support.gc_collect()
+        self.assertFalse(fobj.closed)
+        self.assertEqual(data, fobj.getvalue())
 
 
 class WriteTest(WriteTestBase, unittest.TestCase):
diff --git a/Misc/NEWS b/Misc/NEWS
index a4aaafac62a..9a003f50f59 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -25,6 +25,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #20238: TarFile opened with external fileobj and "w:gz" mode didn't
+  write complete output on close.
+
 - Issue #20245: The open functions in the tarfile module now correctly handle
   empty mode.