diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 2af4f32..402c6e2 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -774,7 +774,7 @@
     loop = futures._get_loop(inner)
     outer = loop.create_future()
 
-    def _done_callback(inner):
+    def _inner_done_callback(inner):
         if outer.cancelled():
             if not inner.cancelled():
                 # Mark inner's result as retrieved.
@@ -790,7 +790,13 @@
             else:
                 outer.set_result(inner.result())
 
-    inner.add_done_callback(_done_callback)
+
+    def _outer_done_callback(outer):
+        if not inner.done():
+            inner.remove_done_callback(_inner_done_callback)
+
+    inner.add_done_callback(_inner_done_callback)
+    outer.add_done_callback(_outer_done_callback)
     return outer
 
 
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index d92ed32..e0dbc95 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -1745,7 +1745,7 @@
         test_utils.run_briefly(self.loop)
         self.assertIs(outer.exception(), exc)
 
-    def test_shield_cancel(self):
+    def test_shield_cancel_inner(self):
         inner = self.new_future(self.loop)
         outer = asyncio.shield(inner)
         test_utils.run_briefly(self.loop)
@@ -1753,6 +1753,15 @@
         test_utils.run_briefly(self.loop)
         self.assertTrue(outer.cancelled())
 
+    def test_shield_cancel_outer(self):
+        inner = self.new_future(self.loop)
+        outer = asyncio.shield(inner)
+        test_utils.run_briefly(self.loop)
+        outer.cancel()
+        test_utils.run_briefly(self.loop)
+        self.assertTrue(outer.cancelled())
+        self.assertEqual(0, 0 if outer._callbacks is None else len(outer._callbacks))
+
     def test_shield_shortcut(self):
         fut = self.new_future(self.loop)
         fut.set_result(42)
diff --git a/Misc/NEWS.d/next/Library/2019-02-15-17-18-50.bpo-35125.h0xk0f.rst b/Misc/NEWS.d/next/Library/2019-02-15-17-18-50.bpo-35125.h0xk0f.rst
new file mode 100644
index 0000000..2e28a25
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-02-15-17-18-50.bpo-35125.h0xk0f.rst
@@ -0,0 +1 @@
+Asyncio: Remove inner callback on outer cancellation in shield