diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 4e67eba4ecac40..a82691a37344f9 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -59,7 +59,7 @@ const {
   kIncomingMessage,
   _checkIsHttpToken: checkIsHttpToken,
 } = require('_http_common');
-const { kServerResponse } = require('_http_server');
+const { kServerResponse, Server: HttpServer, httpServerPreClose, setupConnectionsTracking } = require('_http_server');
 const JSStreamSocket = require('internal/js_stream_socket');
 
 const {
@@ -3180,6 +3180,11 @@ class Http2SecureServer extends TLSServer {
     this[kOptions] = options;
     this.timeout = 0;
     this.on('newListener', setupCompat);
+    if (options.allowHTTP1 === true) {
+      this.headersTimeout = 60_000; // Minimum between 60 seconds or requestTimeout
+      this.requestTimeout = 300_000; // 5 minutes
+      this.on('listening', setupConnectionsTracking);
+    }
     if (typeof requestListener === 'function')
       this.on('request', requestListener);
     this.on('tlsClientError', onErrorSecureServerSession);
@@ -3199,6 +3204,19 @@ class Http2SecureServer extends TLSServer {
     validateSettings(settings);
     this[kOptions].settings = { ...this[kOptions].settings, ...settings };
   }
+
+  close() {
+    if (this[kOptions].allowHTTP1 === true) {
+      httpServerPreClose(this);
+    }
+    ReflectApply(TLSServer.prototype.close, this, arguments);
+  }
+
+  closeIdleConnections() {
+    if (this[kOptions].allowHTTP1 === true) {
+      ReflectApply(HttpServer.prototype.closeIdleConnections, this, arguments);
+    }
+  }
 }
 
 class Http2Server extends NETServer {
diff --git a/test/parallel/test-http2-allow-http1.js b/test/parallel/test-http2-allow-http1.js
new file mode 100644
index 00000000000000..8352aaeb072091
--- /dev/null
+++ b/test/parallel/test-http2-allow-http1.js
@@ -0,0 +1,53 @@
+'use strict';
+
+const common = require('../common');
+const fixtures = require('../common/fixtures');
+if (!common.hasCrypto) common.skip('missing crypto');
+
+const assert = require('assert');
+const https = require('https');
+const http2 = require('http2');
+
+(async function main() {
+  const server = http2.createSecureServer({
+    key: fixtures.readKey('agent1-key.pem'),
+    cert: fixtures.readKey('agent1-cert.pem'),
+    allowHTTP1: true,
+  });
+
+  server.on(
+    'request',
+    common.mustCall((req, res) => {
+      res.writeHead(200);
+      res.end();
+    })
+  );
+
+  server.on(
+    'close',
+    common.mustCall(() => {})
+  );
+
+  await new Promise((resolve) => server.listen(0, resolve));
+
+  await new Promise((resolve) =>
+    https.get(
+      `https://localhost:${server.address().port}`,
+      {
+        rejectUnauthorized: false,
+        headers: { connection: 'keep-alive' },
+      },
+      resolve
+    )
+  );
+
+  let serverClosed = false;
+  setImmediate(common.mustCall(() => {
+    assert.ok(serverClosed, 'server should been closed immediately');
+  }));
+  server.close(
+    common.mustSucceed(() => {
+      serverClosed = true;
+    })
+  );
+})();