diff --git a/Lib/_pyio.py b/Lib/_pyio.py
index f1611a48261..1df44ccbba7 100644
--- a/Lib/_pyio.py
+++ b/Lib/_pyio.py
@@ -1291,8 +1291,10 @@ def flush(self):
         return self.writer.flush()
 
     def close(self):
-        self.writer.close()
-        self.reader.close()
+        try:
+            self.writer.close()
+        finally:
+            self.reader.close()
 
     def isatty(self):
         return self.reader.isatty() or self.writer.isatty()
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
index e5c6073ba32..6a41ae62d9c 100644
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -1649,6 +1649,53 @@ def test_close_and_closed(self):
         pair.close()
         self.assertTrue(pair.closed)
 
+    def test_reader_close_error_on_close(self):
+        def reader_close():
+            reader_non_existing
+        reader = self.MockRawIO()
+        reader.close = reader_close
+        writer = self.MockRawIO()
+        pair = self.tp(reader, writer)
+        with self.assertRaises(NameError) as err:
+            pair.close()
+        self.assertIn('reader_non_existing', str(err.exception))
+        self.assertTrue(pair.closed)
+        self.assertFalse(reader.closed)
+        self.assertTrue(writer.closed)
+
+    def test_writer_close_error_on_close(self):
+        def writer_close():
+            writer_non_existing
+        reader = self.MockRawIO()
+        writer = self.MockRawIO()
+        writer.close = writer_close
+        pair = self.tp(reader, writer)
+        with self.assertRaises(NameError) as err:
+            pair.close()
+        self.assertIn('writer_non_existing', str(err.exception))
+        self.assertFalse(pair.closed)
+        self.assertTrue(reader.closed)
+        self.assertFalse(writer.closed)
+
+    def test_reader_writer_close_error_on_close(self):
+        def reader_close():
+            reader_non_existing
+        def writer_close():
+            writer_non_existing
+        reader = self.MockRawIO()
+        reader.close = reader_close
+        writer = self.MockRawIO()
+        writer.close = writer_close
+        pair = self.tp(reader, writer)
+        with self.assertRaises(NameError) as err:
+            pair.close()
+        self.assertIn('reader_non_existing', str(err.exception))
+        self.assertIsInstance(err.exception.__context__, NameError)
+        self.assertIn('writer_non_existing', str(err.exception.__context__))
+        self.assertFalse(pair.closed)
+        self.assertFalse(reader.closed)
+        self.assertFalse(writer.closed)
+
     def test_isatty(self):
         class SelectableIsAtty(MockRawIO):
             def __init__(self, isatty):
diff --git a/Misc/NEWS b/Misc/NEWS
index c1489983a3c..b85eeafe880 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -30,6 +30,9 @@ Core and Builtins
 Library
 -------
 
+- Issue #21802: The reader in BufferedRWPair now is closed even when closing
+  writer failed in BufferedRWPair.close().
+
 - Issue #23622: Unknown escapes in regular expressions that consist of ``'\'``
   and ASCII letter now raise a deprecation warning and will be forbidden in
   Python 3.6.
diff --git a/Modules/_io/bufferedio.c b/Modules/_io/bufferedio.c
index 358a94dce27..ea9f5332a4a 100644
--- a/Modules/_io/bufferedio.c
+++ b/Modules/_io/bufferedio.c
@@ -2413,12 +2413,18 @@ bufferedrwpair_writable(rwpair *self, PyObject *args)
 static PyObject *
 bufferedrwpair_close(rwpair *self, PyObject *args)
 {
+    PyObject *exc = NULL, *val, *tb;
     PyObject *ret = _forward_call(self->writer, &PyId_close, args);
     if (ret == NULL)
-        return NULL;
-    Py_DECREF(ret);
-
-    return _forward_call(self->reader, &PyId_close, args);
+        PyErr_Fetch(&exc, &val, &tb);
+    else
+        Py_DECREF(ret);
+    ret = _forward_call(self->reader, &PyId_close, args);
+    if (exc != NULL) {
+        _PyErr_ChainExceptions(exc, val, tb);
+        Py_CLEAR(ret);
+    }
+    return ret;
 }
 
 static PyObject *