diff --git a/lib/internal/http2/util.js b/lib/internal/http2/util.js
index fe8542e24f..9441f3e461 100644
--- a/lib/internal/http2/util.js
+++ b/lib/internal/http2/util.js
@@ -127,8 +127,11 @@ function getStreamState(session, stream) {
 function isIllegalConnectionSpecificHeader(name, value) {
   switch (name) {
     case 'connection':
-    case 'upgrade':
     case 'http2-settings':
+    case 'keep-alive':
+    case 'proxy-connection':
+    case 'transfer-encoding':
+    case 'upgrade':
       return true;
     case 'te':
       return value !== 'trailers';
@@ -154,6 +157,7 @@ function mapToHeaders(map) {
     var val;
     if (typeof key === 'symbol' || value === undefined || !key)
       continue;
+    key = String(key).toLowerCase();
     var isArray = Array.isArray(value);
     if (key[0] === ':') {
       if (isArray) {
diff --git a/test/parallel/test-http2-util-headers-list.js b/test/parallel/test-http2-util-headers-list.js
index 8799353e99..c86c72ec65 100644
--- a/test/parallel/test-http2-util-headers-list.js
+++ b/test/parallel/test-http2-util-headers-list.js
@@ -98,12 +98,27 @@ assert.throws(() => mapToHeaders({':path': [1, 2, 3]}),
                 message: /^HTTP\/2 pseudo-headers must have a single value$/
               }));
 
-['connection', 'upgrade', 'http2-settings', 'te'].forEach((i) => {
-  assert.throws(() => mapToHeaders({[i]: 'abc'}),
-                common.expectsError({
-                  code: 'ERR_HTTP2_INVALID_CONNECTION_HEADERS',
-                  message: /^HTTP\/1 Connection specific headers are forbidden$/
-                }));
-});
+const regex =
+  /^HTTP\/1 Connection specific headers are forbidden$/;
+['connection',
+ 'upgrade',
+ 'http2-settings',
+ 'te',
+ 'transfer-encoding',
+ 'proxy-connection',
+ 'keep-alive',
+ 'Connection',
+ 'Upgrade',
+ 'HTTP2-Settings',
+ 'TE',
+ 'Transfer-Encoding',
+ 'Proxy-Connection',
+ 'Keep-Alive'].forEach((i) => {
+   assert.throws(() => mapToHeaders({[i]: 'abc'}),
+                 common.expectsError({
+                   code: 'ERR_HTTP2_INVALID_CONNECTION_HEADERS',
+                   message: regex
+                 }), i);
+ });
 
 assert.doesNotThrow(() => mapToHeaders({ te: 'trailers' }));