diff --git a/docs/versionhistory.rst b/docs/versionhistory.rst
index 72903aea..d99d30a2 100644
--- a/docs/versionhistory.rst
+++ b/docs/versionhistory.rst
@@ -29,6 +29,9 @@ This library adheres to `Semantic Versioning 2.0 <http://semver.org/>`_.
 - Fixed ``to_process.run_sync()`` failing to initialize if ``__main__.__file__`` pointed
   to a file in a nonexistent directory
   (`#696 <https://github.com/agronholm/anyio/issues/696>`_)
+- Fixed ``AssertionError: feed_data after feed_eof`` on asyncio when a subprocess is
+  closed early, before its output has been read
+  (`#490 <https://github.com/agronholm/anyio/issues/490>`_)
 - Fixed ``TaskInfo.has_pending_cancellation()`` on asyncio not respecting shielded
   scopes (`#771 <https://github.com/agronholm/anyio/issues/771>`_; PR by @gschaffner)
 - Fixed ``SocketStream.receive()`` returning ``bytearray`` instead of ``bytes`` when
diff --git a/src/anyio/_backends/_asyncio.py b/src/anyio/_backends/_asyncio.py
index b88b9cc1..97edb8ad 100644
--- a/src/anyio/_backends/_asyncio.py
+++ b/src/anyio/_backends/_asyncio.py
@@ -930,7 +930,7 @@ async def receive(self, max_bytes: int = 65536) -> bytes:
             raise EndOfStream
 
     async def aclose(self) -> None:
-        self._stream.feed_eof()
+        self._stream.set_exception(ClosedResourceError())
         await AsyncIOBackend.checkpoint()
 
 
diff --git a/tests/test_subprocesses.py b/tests/test_subprocesses.py
index 84c4b4dc..e8020a7c 100644
--- a/tests/test_subprocesses.py
+++ b/tests/test_subprocesses.py
@@ -13,7 +13,13 @@
 import pytest
 from pytest import FixtureRequest
 
-from anyio import CancelScope, ClosedResourceError, open_process, run_process
+from anyio import (
+    CancelScope,
+    ClosedResourceError,
+    create_task_group,
+    open_process,
+    run_process,
+)
 from anyio.streams.buffered import BufferedByteReceiveStream
 
 pytestmark = pytest.mark.anyio
@@ -289,3 +295,33 @@ async def test_py39_arguments(
                 pytest.skip(f"the {argname!r} argument is not supported by uvloop yet")
 
             raise
+
+
+async def test_close_early() -> None:
+    """Regression test for #490."""
+    code = dedent("""\
+    import sys
+    for _ in range(100):
+        sys.stdout.buffer.write(bytes(range(256)))
+    """)
+
+    async with await open_process([sys.executable, "-c", code]):
+        pass
+
+
+async def test_close_while_reading() -> None:
+    code = dedent("""\
+    import time
+
+    time.sleep(3)
+    """)
+
+    async with await open_process(
+        [sys.executable, "-c", code]
+    ) as process, create_task_group() as tg:
+        assert process.stdout
+        tg.start_soon(process.stdout.aclose)
+        with pytest.raises(ClosedResourceError):
+            await process.stdout.receive()
+
+        process.terminate()