diff --git a/Lib/multiprocessing/pool.py b/Lib/multiprocessing/pool.py
index f979890170b1a1..b5d17746e21a1e 100644
--- a/Lib/multiprocessing/pool.py
+++ b/Lib/multiprocessing/pool.py
@@ -595,6 +595,9 @@ def _handle_results(outqueue, get, cache):
                 cache[job]._set(i, obj)
             except KeyError:
                 pass
+            except Exception:
+                # Even if we raised we still want to handle callbacks
+                traceback.print_exc()
             task = job = obj = None
 
         while cache and thread._state != TERMINATE:
@@ -612,6 +615,9 @@ def _handle_results(outqueue, get, cache):
                 cache[job]._set(i, obj)
             except KeyError:
                 pass
+            except Exception:
+                # Even if we raised we still want to handle callbacks
+                traceback.print_exc()
             task = job = obj = None
 
         if hasattr(outqueue, '_reader'):
@@ -775,13 +781,15 @@ def get(self, timeout=None):
 
     def _set(self, i, obj):
         self._success, self._value = obj
-        if self._callback and self._success:
-            self._callback(self._value)
-        if self._error_callback and not self._success:
-            self._error_callback(self._value)
-        self._event.set()
-        del self._cache[self._job]
-        self._pool = None
+        try:
+            if self._callback and self._success:
+                self._callback(self._value)
+            if self._error_callback and not self._success:
+                self._error_callback(self._value)
+        finally:
+            self._event.set()
+            del self._cache[self._job]
+            self._pool = None
 
     __class_getitem__ = classmethod(types.GenericAlias)
 
@@ -812,11 +820,13 @@ def _set(self, i, success_result):
         if success and self._success:
             self._value[i*self._chunksize:(i+1)*self._chunksize] = result
             if self._number_left == 0:
-                if self._callback:
-                    self._callback(self._value)
-                del self._cache[self._job]
-                self._event.set()
-                self._pool = None
+                try:
+                    if self._callback:
+                        self._callback(self._value)
+                finally:
+                    del self._cache[self._job]
+                    self._event.set()
+                    self._pool = None
         else:
             if not success and self._success:
                 # only store first exception
@@ -824,11 +834,13 @@ def _set(self, i, success_result):
                 self._value = result
             if self._number_left == 0:
                 # only consider the result ready once all jobs are done
-                if self._error_callback:
-                    self._error_callback(self._value)
-                del self._cache[self._job]
-                self._event.set()
-                self._pool = None
+                try:
+                    if self._error_callback:
+                        self._error_callback(self._value)
+                finally:
+                    del self._cache[self._job]
+                    self._event.set()
+                    self._pool = None
 
 #
 # Class whose instances are returned by `Pool.imap()`
diff --git a/Lib/test/_test_multiprocessing.py b/Lib/test/_test_multiprocessing.py
index 69174cff699115..8eafc9611f563b 100644
--- a/Lib/test/_test_multiprocessing.py
+++ b/Lib/test/_test_multiprocessing.py
@@ -3336,6 +3336,39 @@ def errback(exc):
         p.close()
         p.join()
 
+class _TestPoolResultHandlerErrors(BaseTestCase):
+    ALLOWED_TYPES = ('processes', )
+
+    def test_apply_async_callback_raises_exception(self):
+        p = multiprocessing.Pool(1)
+
+        def job():
+            return 1
+
+        def callback(value):
+            raise Exception()
+
+        p.apply_async(job, callback=callback)
+
+        self.assertTrue(p._result_handler.is_alive())
+        p.close()
+        p.join()
+
+    def test_map_async_callback_raises_exception(self):
+        p = multiprocessing.Pool(1)
+
+        def job(value):
+            return value
+
+        def callback(value):
+            raise Exception()
+
+        p.map_async(job, [1], callback=callback)
+
+        self.assertTrue(p._result_handler.is_alive())
+        p.close()
+        p.join()
+
 class _TestPoolWorkerLifetime(BaseTestCase):
     ALLOWED_TYPES = ('processes', )
 
@@ -7346,7 +7379,6 @@ def install_tests_in_module_dict(remote_globs, start_method,
     __module__ = remote_globs['__name__']
     local_globs = globals()
     ALL_TYPES = {'processes', 'threads', 'manager'}
-
     for name, base in local_globs.items():
         if not isinstance(base, type):
             continue
diff --git a/Misc/NEWS.d/next/Library/2020-09-03-09-01-34.bpo-39190.oU-ejc.rst b/Misc/NEWS.d/next/Library/2020-09-03-09-01-34.bpo-39190.oU-ejc.rst
new file mode 100644
index 00000000000000..891aa976882268
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-09-03-09-01-34.bpo-39190.oU-ejc.rst
@@ -0,0 +1 @@
+Fix deadlock when pool.apply_async's and pool.map_async's callbacks raise exception
\ No newline at end of file