diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 8d8f200262d1d9..9bd503a799e4f5 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -1804,6 +1804,13 @@ class ServerHttp2Stream extends Http2Stream {
 
         const stream = new ServerHttp2Stream(session, ret, options, headers);
 
+        if (options.weight !== undefined) {
+          stream.priority({
+            weight: options.weight,
+            silent: true
+          });
+        }
+
         // If the push stream is a head request, close the writable side of
         // the stream immediately as there won't be any data sent.
         if (headRequest) {
diff --git a/test/parallel/test-http2-server-push-priority.js b/test/parallel/test-http2-server-push-priority.js
new file mode 100644
index 00000000000000..e9753ccec48593
--- /dev/null
+++ b/test/parallel/test-http2-server-push-priority.js
@@ -0,0 +1,47 @@
+'use strict';
+
+const common = require('../common');
+if (!common.hasCrypto)
+  common.skip('missing crypto');
+const assert = require('assert');
+const http2 = require('http2');
+
+
+const server = http2.createServer();
+server.on('stream', common.mustCall((stream, headers, flags) => {
+  const expectedWeight = 256;
+  const options = { weight: expectedWeight };
+  stream.pushStream({}, options, common.mustCall((stream, headers, flags) => {
+    // The priority of push streams is changed silently by nghttp2,
+    // without emitting a PRIORITY frame. Flags are ignored.
+    assert.strictEqual(stream.state.weight, expectedWeight);
+    assert.strictEqual(flags & http2.constants.NGHTTP2_FLAG_PRIORITY, 0);
+  }));
+  stream.respond({
+    'content-type': 'text/html',
+    ':status': 200
+  });
+  stream.end('test');
+}));
+
+server.listen(0, common.mustCall(() => {
+  const port = server.address().port;
+  const client = http2.connect(`http://localhost:${port}`);
+
+  const headers = { ':path': '/' };
+  const req = client.request(headers);
+
+  client.on('stream', common.mustCall((stream, headers, flags) => {
+    // Since the push priority is set silently, the client is not informed.
+    const expectedWeight = http2.constants.NGHTTP2_DEFAULT_WEIGHT;
+    assert.strictEqual(stream.state.weight, expectedWeight);
+    assert.strictEqual(flags & http2.constants.NGHTTP2_FLAG_PRIORITY, 0);
+  }));
+
+  req.on('data', common.mustCall(() => {}));
+  req.on('end', common.mustCall(() => {
+    server.close();
+    client.destroy();
+  }));
+  req.end();
+}));