diff --git a/tests/protocols/test_http.py b/tests/protocols/test_http.py
index 45ccc1d23..db196d99c 100644
--- a/tests/protocols/test_http.py
+++ b/tests/protocols/test_http.py
@@ -61,6 +61,20 @@
 
 CONNECTION_CLOSE_REQUEST = b"\r\n".join([b"GET / HTTP/1.1", b"Host: example.org", b"Connection: close", b"", b""])
 
+REQUEST_AFTER_CONNECTION_CLOSE = b"\r\n".join(
+    [
+        b"GET / HTTP/1.1",
+        b"Host: example.org",
+        b"Connection: close",
+        b"",
+        b"",
+        b"GET / HTTP/1.1",
+        b"Host: example.org",
+        b"",
+        b"",
+    ]
+)
+
 LARGE_POST_REQUEST = b"\r\n".join(
     [
         b"POST / HTTP/1.1",
@@ -983,6 +997,20 @@ async def test_return_close_header(http_protocol_cls: HTTPProtocol):
     assert b"connection: close" in protocol.transport.buffer.lower()
 
 
+async def test_close_connection_with_multiple_requests(http_protocol_cls: HTTPProtocol):
+    app = Response("Hello, world", media_type="text/plain")
+
+    protocol = get_connected_protocol(app, http_protocol_cls)
+    protocol.data_received(REQUEST_AFTER_CONNECTION_CLOSE)
+    await protocol.loop.run_one()
+    assert b"HTTP/1.1 200 OK" in protocol.transport.buffer
+    assert b"content-type: text/plain" in protocol.transport.buffer
+    assert b"content-length: 12" in protocol.transport.buffer
+    # NOTE: We need to use `.lower()` because H11 implementation doesn't allow Uvicorn
+    # to lowercase them. See: https://github.com/python-hyper/h11/issues/156
+    assert b"connection: close" in protocol.transport.buffer.lower()
+
+
 async def test_iterator_headers(http_protocol_cls: HTTPProtocol):
     async def app(scope: Scope, receive: ASGIReceiveCallable, send: ASGISendCallable):
         headers = iter([(b"x-test-header", b"test value")])
diff --git a/uvicorn/protocols/http/h11_impl.py b/uvicorn/protocols/http/h11_impl.py
index 9d2a2dabd..04d51dfdb 100644
--- a/uvicorn/protocols/http/h11_impl.py
+++ b/uvicorn/protocols/http/h11_impl.py
@@ -259,6 +259,8 @@ def handle_events(self) -> None:
                     self.transport.resume_reading()
                     self.conn.start_next_cycle()
                     continue
+                if self.conn.their_state == h11.MUST_CLOSE:
+                    break
                 self.cycle.more_body = False
                 self.cycle.message_event.set()