diff --git a/http2/server.go b/http2/server.go
index 793899169..e111019d5 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -1721,6 +1721,13 @@ func (sc *serverConn) processHeaders(f *MetaHeadersFrame) error {
 			// processing this frame.
 			return nil
 		}
+		// RFC 7540, sec 5.1: If an endpoint receives additional frames, other than
+		// WINDOW_UPDATE, PRIORITY, or RST_STREAM, for a stream that is in
+		// this state, it MUST respond with a stream error (Section 5.4.2) of
+		// type STREAM_CLOSED.
+		if st.state == stateHalfClosedRemote {
+			return streamError(id, ErrCodeStreamClosed)
+		}
 		return st.processTrailerHeaders(f)
 	}
 
diff --git a/http2/server_test.go b/http2/server_test.go
index 9c3e549dc..157388973 100644
--- a/http2/server_test.go
+++ b/http2/server_test.go
@@ -3841,3 +3841,51 @@ func TestServerHandlerConnectionClose(t *testing.T) {
 		}
 	})
 }
+
+func TestServer_Headers_HalfCloseRemote(t *testing.T) {
+	var st *serverTester
+	inHandler := make(chan bool)
+	writeHeaders := make(chan bool)
+	leaveHandler := make(chan bool)
+	st = newServerTester(t, func(w http.ResponseWriter, r *http.Request) {
+		inHandler <- true
+		if st.stream(1) == nil {
+			t.Errorf("nil stream 1 in handler")
+		}
+		if got, want := st.streamState(1), stateOpen; got != want {
+			t.Errorf("in handler, state is %v; want %v", got, want)
+		}
+		if n, err := r.Body.Read(make([]byte, 1)); n != 0 || err != io.EOF {
+			t.Errorf("body read = %d, %v; want 0, EOF", n, err)
+		}
+		if got, want := st.streamState(1), stateHalfClosedRemote; got != want {
+			t.Errorf("in handler, state is %v; want %v", got, want)
+		}
+		writeHeaders <- true
+
+		<-leaveHandler
+	})
+	st.greet()
+
+	st.writeHeaders(HeadersFrameParam{
+		StreamID:      1,
+		BlockFragment: st.encodeHeader(),
+		EndStream:     false, // keep it open
+		EndHeaders:    true,
+	})
+	<-inHandler
+	st.writeData(1, true, nil)
+
+	<-writeHeaders
+
+	st.writeHeaders(HeadersFrameParam{
+		StreamID:      1,
+		BlockFragment: st.encodeHeader(),
+		EndStream:     false, // keep it open
+		EndHeaders:    true,
+	})
+
+	defer close(leaveHandler)
+
+	st.wantRSTStream(1, ErrCodeStreamClosed)
+}