diff --git a/src/codec/framed_read.rs b/src/codec/framed_read.rs
index e65b2dad9..be5d5c75b 100644
--- a/src/codec/framed_read.rs
+++ b/src/codec/framed_read.rs
@@ -253,7 +253,7 @@ fn decode_frame(
             .into()
         }
         Kind::GoAway => {
-            let res = frame::GoAway::load(&bytes[frame::HEADER_LEN..]);
+            let res = frame::GoAway::load(head, &bytes[frame::HEADER_LEN..]);
             res.map_err(|e| {
                 proto_err!(conn: "failed to load GO_AWAY frame; err={:?}", e);
                 Error::library_go_away(Reason::PROTOCOL_ERROR)
diff --git a/src/frame/go_away.rs b/src/frame/go_away.rs
index 99330e981..8f234645c 100644
--- a/src/frame/go_away.rs
+++ b/src/frame/go_away.rs
@@ -40,7 +40,17 @@ impl GoAway {
         &self.debug_data
     }
 
-    pub fn load(payload: &[u8]) -> Result<GoAway, Error> {
+    pub fn load(head: Head, payload: &[u8]) -> Result<GoAway, Error> {
+        debug_assert_eq!(head.kind(), crate::frame::Kind::GoAway);
+
+        // The GOAWAY frame applies to the connection, not a specific stream.
+        // An endpoint MUST treat a GOAWAY frame with a stream identifier
+        // other than 0x00 as a connection error (Section 5.4.1) of type
+        // PROTOCOL_ERROR.
+        if !head.stream_id().is_zero() {
+            return Err(Error::InvalidStreamId);
+        }
+
         if payload.len() < 8 {
             return Err(Error::BadFrameSize);
         }
diff --git a/src/frame/mod.rs b/src/frame/mod.rs
index ab8c43c1b..4a0c03036 100644
--- a/src/frame/mod.rs
+++ b/src/frame/mod.rs
@@ -153,8 +153,8 @@ pub enum Error {
 
     /// An invalid stream identifier was provided.
     ///
-    /// This is returned if a SETTINGS or PING frame is received with a stream
-    /// identifier other than zero.
+    /// This is returned if a SETTINGS, PING or GOAWAY frame is received with a
+    /// stream identifier other than zero.
     InvalidStreamId,
 
     /// A request or response is malformed.
diff --git a/tests/h2-tests/tests/codec_read.rs b/tests/h2-tests/tests/codec_read.rs
index 489d16daf..98ab122ba 100644
--- a/tests/h2-tests/tests/codec_read.rs
+++ b/tests/h2-tests/tests/codec_read.rs
@@ -239,3 +239,19 @@ async fn read_goaway_with_debug_data() {
 
     assert_closed!(codec);
 }
+
+#[tokio::test]
+async fn read_goaway_stream_id_not_zero() {
+    let mut codec = raw_codec! {
+        read => [
+            // head, stream id 1
+            0, 0, 8, 7, 0, 0, 0, 0, 1,
+            // last_stream_id
+            0, 0, 0, 0,
+            // error_code
+            0, 0, 0, 0,
+        ];
+    };
+
+    poll_err!(codec);
+}