diff --git a/Lib/tempfile.py b/Lib/tempfile.py
index 448163f04380d5..dbc10a300f8799 100644
--- a/Lib/tempfile.py
+++ b/Lib/tempfile.py
@@ -543,12 +543,18 @@ def NamedTemporaryFile(mode='w+b', buffering=-1, encoding=None,
         file = _io.open(fd, mode, buffering=buffering,
                         newline=newline, encoding=encoding, errors=errors)
 
-        return _TemporaryFileWrapper(file, name, delete)
     except BaseException:
         _os.unlink(name)
         _os.close(fd)
         raise
 
+    try:
+        return _TemporaryFileWrapper(file, name, delete)
+    except BaseException:
+        _os.unlink(name)
+        file.close()
+        raise
+
 if _os.name != 'posix' or _sys.platform == 'cygwin':
     # On non-POSIX and Cygwin systems, assume that we cannot unlink a file
     # while it is open.
diff --git a/Misc/NEWS.d/next/Library/2020-01-13-13-36-05.bpo-39318.236VwO.rst b/Misc/NEWS.d/next/Library/2020-01-13-13-36-05.bpo-39318.236VwO.rst
new file mode 100644
index 00000000000000..7ce343179c3ba6
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-01-13-13-36-05.bpo-39318.236VwO.rst
@@ -0,0 +1 @@
+Fix a file descriptor leak in NamedTemporaryFile under unusual circumstances.
\ No newline at end of file