diff --git a/Doc/library/asyncio-task.rst b/Doc/library/asyncio-task.rst
index 4892333d8ce..233cc945496 100644
--- a/Doc/library/asyncio-task.rst
+++ b/Doc/library/asyncio-task.rst
@@ -443,6 +443,8 @@ Task
       Return a set of all tasks for an event loop.
 
       By default all tasks for the current event loop are returned.
+      If *loop* is ``None``, :func:`get_event_loop` function
+      is used to get the current loop.
 
    .. classmethod:: current_task(loop=None)
 
@@ -567,8 +569,9 @@ Task functions
 
    Return a set of :class:`Task` objects created for the loop.
 
-   If *loop* is ``None`` :func:`get_event_loop` is used for getting
-   current loop.
+   If *loop* is ``None``, :func:`get_running_loop` is used for getting
+   current loop (contrary to the deprecated :meth:`Task.all_tasks` method
+   that uses :func:`get_event_loop`.)
 
    .. versionadded:: 3.7
 
diff --git a/Lib/asyncio/__init__.py b/Lib/asyncio/__init__.py
index 23ea055912e..26859024300 100644
--- a/Lib/asyncio/__init__.py
+++ b/Lib/asyncio/__init__.py
@@ -18,6 +18,10 @@ from .subprocess import *
 from .tasks import *
 from .transports import *
 
+# Exposed for _asynciomodule.c to implement now deprecated
+# Task.all_tasks() method.  This function will be removed in 3.9.
+from .tasks import _all_tasks_compat  # NoQA
+
 __all__ = (base_events.__all__ +
            coroutines.__all__ +
            events.__all__ +
diff --git a/Lib/asyncio/runners.py b/Lib/asyncio/runners.py
index bb54b725278..5fbab03dd00 100644
--- a/Lib/asyncio/runners.py
+++ b/Lib/asyncio/runners.py
@@ -51,8 +51,7 @@ def run(main, *, debug=False):
 
 
 def _cancel_all_tasks(loop):
-    to_cancel = [task for task in tasks.all_tasks(loop)
-                 if not task.done()]
+    to_cancel = tasks.all_tasks(loop)
     if not to_cancel:
         return
 
diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 4a9db2a3a05..67fb57c6a78 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -33,6 +33,16 @@ def current_task(loop=None):
 
 def all_tasks(loop=None):
     """Return a set of all tasks for the loop."""
+    if loop is None:
+        loop = events.get_running_loop()
+    return {t for t in _all_tasks
+            if futures._get_loop(t) is loop and not t.done()}
+
+
+def _all_tasks_compat(loop=None):
+    # Different from "all_task()" by returning *all* Tasks, including
+    # the completed ones.  Used to implement deprecated "Tasks.all_task()"
+    # method.
     if loop is None:
         loop = events.get_event_loop()
     return {t for t in _all_tasks if futures._get_loop(t) is loop}
@@ -82,7 +92,7 @@ class Task(futures._PyFuture):  # Inherit Python Task implementation
                       "use asyncio.all_tasks() instead",
                       PendingDeprecationWarning,
                       stacklevel=2)
-        return all_tasks(loop)
+        return _all_tasks_compat(loop)
 
     def __init__(self, coro, *, loop=None):
         super().__init__(loop=loop)
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index e5334c6ff91..33300c91a36 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -1897,8 +1897,10 @@ class BaseTaskTests:
         # See http://bugs.python.org/issue29271 for details:
         asyncio.set_event_loop(self.loop)
         try:
-            self.assertEqual(asyncio.all_tasks(), {task})
-            self.assertEqual(asyncio.all_tasks(None), {task})
+            with self.assertWarns(PendingDeprecationWarning):
+                self.assertEqual(Task.all_tasks(), {task})
+            with self.assertWarns(PendingDeprecationWarning):
+                self.assertEqual(Task.all_tasks(None), {task})
         finally:
             asyncio.set_event_loop(None)
 
@@ -2483,6 +2485,9 @@ class BaseTaskIntrospectionTests:
             def _loop(self):
                 return loop
 
+            def done(self):
+                return False
+
         task = TaskLike()
         loop = mock.Mock()
 
@@ -2496,6 +2501,9 @@ class BaseTaskIntrospectionTests:
             def get_loop(self):
                 return loop
 
+            def done(self):
+                return False
+
         task = TaskLike()
         loop = mock.Mock()
 
@@ -2504,6 +2512,23 @@ class BaseTaskIntrospectionTests:
         self.assertEqual(asyncio.all_tasks(loop), {task})
         self._unregister_task(task)
 
+    def test__register_task_3(self):
+        class TaskLike:
+            def get_loop(self):
+                return loop
+
+            def done(self):
+                return True
+
+        task = TaskLike()
+        loop = mock.Mock()
+
+        self.assertEqual(asyncio.all_tasks(loop), set())
+        self._register_task(task)
+        self.assertEqual(asyncio.all_tasks(loop), set())
+        self.assertEqual(asyncio.Task.all_tasks(loop), {task})
+        self._unregister_task(task)
+
     def test__enter_task(self):
         task = mock.Mock()
         loop = mock.Mock()
diff --git a/Misc/NEWS.d/next/Library/2018-05-28-16-40-32.bpo-32610.KvUAsL.rst b/Misc/NEWS.d/next/Library/2018-05-28-16-40-32.bpo-32610.KvUAsL.rst
new file mode 100644
index 00000000000..37290806324
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2018-05-28-16-40-32.bpo-32610.KvUAsL.rst
@@ -0,0 +1 @@
+Make asyncio.all_tasks() return only pending tasks.
diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index c4d19034ce4..e3537cc81c4 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -11,7 +11,7 @@ module _asyncio
 /* identifiers used from some functions */
 _Py_IDENTIFIER(__asyncio_running_event_loop__);
 _Py_IDENTIFIER(add_done_callback);
-_Py_IDENTIFIER(all_tasks);
+_Py_IDENTIFIER(_all_tasks_compat);
 _Py_IDENTIFIER(call_soon);
 _Py_IDENTIFIER(cancel);
 _Py_IDENTIFIER(current_task);
@@ -2125,7 +2125,7 @@ _asyncio_Task_all_tasks_impl(PyTypeObject *type, PyObject *loop)
         return NULL;
     }
 
-    all_tasks_func = _PyObject_GetAttrId(asyncio_mod, &PyId_all_tasks);
+    all_tasks_func = _PyObject_GetAttrId(asyncio_mod, &PyId__all_tasks_compat);
     if (all_tasks_func == NULL) {
         return NULL;
     }