diff --git a/lib/internal/http2/compat.js b/lib/internal/http2/compat.js
index 2437009486668c..a02d3b0c5844fa 100644
--- a/lib/internal/http2/compat.js
+++ b/lib/internal/http2/compat.js
@@ -706,7 +706,7 @@ class Http2ServerResponse extends Stream {
   writeHead(statusCode, statusMessage, headers) {
     const state = this[kState];
 
-    if (state.closed || this.stream.destroyed)
+    if (state.closed || this.stream.destroyed || this.stream.closed)
       return this;
     if (this[kStream].headersSent)
       throw new ERR_HTTP2_HEADERS_SENT();
diff --git a/test/parallel/test-http2-compat-write-head-after-close.js b/test/parallel/test-http2-compat-write-head-after-close.js
new file mode 100644
index 00000000000000..541973f5dbc5c6
--- /dev/null
+++ b/test/parallel/test-http2-compat-write-head-after-close.js
@@ -0,0 +1,23 @@
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto) { common.skip('missing crypto'); };
+const h2 = require('http2');
+
+const server = h2.createServer((req, res) => {
+  const stream = req.stream;
+  stream.close();
+  res.writeHead(200, { 'content-type': 'text/plain' });
+});
+
+server.listen(0, common.mustCall(() => {
+  const port = server.address().port;
+  const client = h2.connect(`http://localhost:${port}`);
+  const req = client.request({ ':path': '/' });
+  req.on('response', common.mustNotCall('head after close should not be sent'));
+  req.on('end', common.mustCall(() => {
+    client.close();
+    server.close();
+  }));
+  req.end();
+}));