diff --git a/starlette/background.py b/starlette/background.py
index 1160baeed..d0a186d74 100644
--- a/starlette/background.py
+++ b/starlette/background.py
@@ -1,7 +1,7 @@
-import asyncio
 import typing
 
 from starlette.concurrency import run_in_threadpool
+from starlette.utils import iscoroutinefunction
 
 
 class BackgroundTask:
@@ -11,7 +11,7 @@ def __init__(
         self.func = func
         self.args = args
         self.kwargs = kwargs
-        self.is_async = asyncio.iscoroutinefunction(func)
+        self.is_async = iscoroutinefunction(func)
 
     async def __call__(self) -> None:
         if self.is_async:
diff --git a/starlette/utils.py b/starlette/utils.py
new file mode 100644
index 000000000..c993580e9
--- /dev/null
+++ b/starlette/utils.py
@@ -0,0 +1,7 @@
+import inspect
+
+
+def iscoroutinefunction(obj: object) -> bool:
+    if inspect.iscoroutinefunction(obj):
+        return True
+    return callable(obj) and inspect.iscoroutinefunction(obj.__call__)
diff --git a/tests/test_background.py b/tests/test_background.py
index e299ec362..f59ad966c 100644
--- a/tests/test_background.py
+++ b/tests/test_background.py
@@ -21,6 +21,26 @@ async def app(scope, receive, send):
     assert TASK_COMPLETE
 
 
+def test_async_callable_task(test_client_factory):
+    TASK_COMPLETE = False
+
+    class async_callable_task:
+        async def __call__(self):
+            nonlocal TASK_COMPLETE
+            TASK_COMPLETE = True
+
+    task = BackgroundTask(async_callable_task())
+
+    async def app(scope, receive, send):
+        response = Response("task initiated", media_type="text/plain", background=task)
+        await response(scope, receive, send)
+
+    client = test_client_factory(app)
+    response = client.get("/")
+    assert response.text == "task initiated"
+    assert TASK_COMPLETE
+
+
 def test_sync_task(test_client_factory):
     TASK_COMPLETE = False
 
diff --git a/tests/test_utils.py b/tests/test_utils.py
new file mode 100644
index 000000000..3ba81695c
--- /dev/null
+++ b/tests/test_utils.py
@@ -0,0 +1,31 @@
+from starlette.utils import iscoroutinefunction
+
+
+def test_is_coroutine_function():
+    async def func():
+        pass  # pragma: no cover
+
+    assert iscoroutinefunction(func)
+
+
+def test_is_not_coroutine_function():
+    def func():
+        pass  # pragma: no cover
+
+    assert not iscoroutinefunction(func)
+
+
+def test_is_async_callable():
+    class async_callable_obj:
+        async def __call__(self):
+            pass  # pragma: no cover
+
+    assert iscoroutinefunction(async_callable_obj())
+
+
+def test_is_not_asnyc_callable():
+    class callable_obj:
+        def __call__(self):
+            pass  # pragma: no cover
+
+    assert not iscoroutinefunction(callable_obj())