diff --git a/lib/core/util.js b/lib/core/util.js
index a62396e23e0..e7b5d9c1edd 100644
--- a/lib/core/util.js
+++ b/lib/core/util.js
@@ -246,9 +246,6 @@ function bufferToLowerCasedHeaderName (value) {
  * @returns {Record<string, string | string[]>}
  */
 function parseHeaders (headers, obj) {
-  // For H2 support
-  if (!Array.isArray(headers)) return headers
-
   if (obj === undefined) obj = {}
   for (let i = 0; i < headers.length; i += 2) {
     const key = headerNameToString(headers[i])
diff --git a/lib/dispatcher/client-h2.js b/lib/dispatcher/client-h2.js
index d593eae4fca..0a53b75e501 100644
--- a/lib/dispatcher/client-h2.js
+++ b/lib/dispatcher/client-h2.js
@@ -54,6 +54,20 @@ const {
   }
 } = http2
 
+function parseH2Headers (headers) {
+  // set-cookie is always an array. Duplicates are added to the array.
+  // For duplicate cookie headers, the values are joined together with '; '.
+  headers = Object.entries(headers).flat(2)
+
+  const result = []
+
+  for (const header of headers) {
+    result.push(Buffer.from(header))
+  }
+
+  return result
+}
+
 async function connectH2 (client, socket) {
   client[kSocket] = socket
 
@@ -391,7 +405,7 @@ function writeH2 (client, request) {
     const { [HTTP2_HEADER_STATUS]: statusCode, ...realHeaders } = headers
     request.onResponseStarted()
 
-    if (request.onHeaders(Number(statusCode), realHeaders, stream.resume.bind(stream), '') === false) {
+    if (request.onHeaders(Number(statusCode), parseH2Headers(realHeaders), stream.resume.bind(stream), '') === false) {
       stream.pause()
     }
 
diff --git a/lib/web/fetch/index.js b/lib/web/fetch/index.js
index d8c20c59bf7..58d61585c06 100644
--- a/lib/web/fetch/index.js
+++ b/lib/web/fetch/index.js
@@ -2141,29 +2141,6 @@ async function httpNetworkFetch (
               codings = contentEncoding.toLowerCase().split(',').map((x) => x.trim())
             }
             location = headersList.get('location', true)
-          } else {
-            const keys = Object.keys(rawHeaders)
-            for (let i = 0; i < keys.length; ++i) {
-              // The header names are already in lowercase.
-              const key = keys[i]
-              const value = rawHeaders[key]
-              if (key === 'set-cookie') {
-                for (let j = 0; j < value.length; ++j) {
-                  headersList.append(key, value[j], true)
-                }
-              } else {
-                headersList.append(key, value, true)
-              }
-            }
-            // For H2, The header names are already in lowercase,
-            // so we can avoid the `HeadersList#get` call here.
-            const contentEncoding = rawHeaders['content-encoding']
-            if (contentEncoding) {
-              // https://www.rfc-editor.org/rfc/rfc7231#section-3.1.2.1
-              // "All content-coding values are case-insensitive..."
-              codings = contentEncoding.toLowerCase().split(',').map((x) => x.trim()).reverse()
-            }
-            location = rawHeaders.location
           }
 
           this.body = new Readable({ read: resume })
diff --git a/test/fetch/http2.js b/test/fetch/http2.js
index 0793a21556c..1cef1d00ce6 100644
--- a/test/fetch/http2.js
+++ b/test/fetch/http2.js
@@ -34,7 +34,7 @@ test('[Fetch] Issue#2311', async (t) => {
     res.end(body)
   })
 
-  const { strictEqual } = tspl(t, { plan: 1 })
+  const { strictEqual } = tspl(t, { plan: 2 })
 
   server.listen()
   await once(server, 'listening')
@@ -65,6 +65,7 @@ test('[Fetch] Issue#2311', async (t) => {
   t.after(closeClientAndServerAsPromise(client, server))
 
   strictEqual(responseBody, expectedBody)
+  strictEqual(response.headers.get('x-custom-h2'), 'foo')
 })
 
 test('[Fetch] Simple GET with h2', async (t) => {
diff --git a/test/http2.js b/test/http2.js
index 3319ffddb1e..849a0cc43ba 100644
--- a/test/http2.js
+++ b/test/http2.js
@@ -851,8 +851,10 @@ test('Should handle h2 request with body (string or buffer) - dispatch', async t
         },
         onHeaders (statusCode, headers) {
           t.strictEqual(statusCode, 200)
-          t.strictEqual(headers['content-type'], 'text/plain; charset=utf-8')
-          t.strictEqual(headers['x-custom-h2'], 'foo')
+          t.strictEqual(headers[0].toString('utf-8'), 'content-type')
+          t.strictEqual(headers[1].toString('utf-8'), 'text/plain; charset=utf-8')
+          t.strictEqual(headers[2].toString('utf-8'), 'x-custom-h2')
+          t.strictEqual(headers[3].toString('utf-8'), 'foo')
         },
         onData (chunk) {
           response.push(chunk)