diff --git a/Misc/NEWS b/Misc/NEWS
index 9ed8b16b93f..407681b3d65 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -15,6 +15,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #6271: mmap tried to close invalid file handle (-1) when annonymous.
+  (On Unix)
+
 
 What's New in Python 3.1 Release Candidate 2?
 =============================================
diff --git a/Modules/mmapmodule.c b/Modules/mmapmodule.c
index fd247abd56b..37584e22255 100644
--- a/Modules/mmapmodule.c
+++ b/Modules/mmapmodule.c
@@ -164,7 +164,8 @@ mmap_close_method(mmap_object *self, PyObject *unused)
 #endif /* MS_WINDOWS */
 
 #ifdef UNIX
-	(void) close(self->fd);
+	if (0 <= self->fd)
+		(void) close(self->fd);
 	self->fd = -1;
 	if (self->data != NULL) {
 		munmap(self->data, self->size);