diff --git a/tarfile.py b/tarfile.py
--- a/tarfile.py
+++ b/tarfile.py
@@ -1187,7 +1187,8 @@
         if len(buf) != BLOCKSIZE:
             raise HeaderError("truncated header")
         if buf.count(NUL) == BLOCKSIZE:
-            raise HeaderError("empty header")
+            # This can happen if the tar file is empty
+            return
 
         chksum = nti(buf[148:156])
         if chksum not in calc_chksums(buf):
@@ -1233,6 +1234,9 @@
         if not buf:
             return
         obj = cls.frombuf(buf)
+        if obj is None:
+            # This can happen if the tar file is empty
+            return
         obj.offset = tarfile.fileobj.tell() - BLOCKSIZE
         return obj._proc_member(tarfile)