diff --git a/Lib/concurrent/futures/process.py b/Lib/concurrent/futures/process.py
index 36355ae8756..8e9b69a8f08 100644
--- a/Lib/concurrent/futures/process.py
+++ b/Lib/concurrent/futures/process.py
@@ -728,6 +728,8 @@ def shutdown(self, wait=True, *, cancel_futures=False):
         # objects that use file descriptors.
         self._executor_manager_thread = None
         self._call_queue = None
+        if self._result_queue is not None and wait:
+            self._result_queue.close()
         self._result_queue = None
         self._processes = None
 
diff --git a/Misc/NEWS.d/next/Library/2020-04-27-20-27-39.bpo-30966.Xmtlqu.rst b/Misc/NEWS.d/next/Library/2020-04-27-20-27-39.bpo-30966.Xmtlqu.rst
new file mode 100644
index 00000000000..85b7934ba66
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-04-27-20-27-39.bpo-30966.Xmtlqu.rst
@@ -0,0 +1,2 @@
+``Process.shutdown(wait=True)`` of :mod:`concurrent.futures` now closes
+explicitly the result queue.