diff --git a/lib/client.js b/lib/client.js
index 688df9e6156..f237fe02ab8 100644
--- a/lib/client.js
+++ b/lib/client.js
@@ -569,7 +569,10 @@ class Parser {
         /* istanbul ignore else: difficult to make a test case for */
         if (ptr) {
           const len = new Uint8Array(llhttp.memory.buffer, ptr).indexOf(0)
-          message = Buffer.from(llhttp.memory.buffer, ptr, len).toString()
+          message =
+            'Response does not match the HTTP/1.1 protocol (' +
+            Buffer.from(llhttp.memory.buffer, ptr, len).toString() +
+            ')'
         }
         throw new HTTPParserError(message, constants.ERROR[ret], data.slice(offset))
       }
diff --git a/test/http2.js b/test/http2.js
new file mode 100644
index 00000000000..ab8752a7816
--- /dev/null
+++ b/test/http2.js
@@ -0,0 +1,32 @@
+'use strict'
+
+const { test } = require('tap')
+const { Client, errors } = require('..')
+const { createSecureServer } = require('http2')
+const pem = require('https-pem')
+
+test('throw http2 not supported error', (t) => {
+  t.plan(1)
+
+  const server = createSecureServer({ key: pem.key, cert: pem.cert }, (req, res) => {
+    res.stream.respond({ 'content-type': 'text/plain' })
+    res.stream.end('hello')
+  }).on('unknownProtocol', (socket) => {
+    // continue sending data in http2 to our http1.1 client to trigger error
+    socket.write('PRI * HTTP/2.0\r\n\r\nSM\r\n\r\n')
+  })
+  t.teardown(server.close.bind(server))
+
+  server.listen(0, () => {
+    const client = new Client(`https://localhost:${server.address().port}`, {
+      tls: {
+        rejectUnauthorized: false
+      }
+    })
+    t.teardown(client.close.bind(client))
+
+    client.request({ path: '/', method: 'GET' }, (err, data) => {
+      t.type(err, errors.HTTPParserError)
+    })
+  })
+})
diff --git a/test/parser-issues.js b/test/parser-issues.js
index 7f5bfbb5f99..b98edf159ef 100644
--- a/test/parser-issues.js
+++ b/test/parser-issues.js
@@ -1,6 +1,6 @@
 const net = require('net')
 const { test } = require('tap')
-const { Client } = require('..')
+const { Client, errors } = require('..')
 
 test('https://github.com/mcollina/undici/issues/268', (t) => {
   t.plan(2)
@@ -40,7 +40,7 @@ test('https://github.com/mcollina/undici/issues/268', (t) => {
 })
 
 test('parser fail', (t) => {
-  t.plan(3)
+  t.plan(2)
 
   const server = net.createServer(socket => {
     socket.write('HTT/1.1 200 OK\r\n')
@@ -56,8 +56,7 @@ test('parser fail', (t) => {
       path: '/'
     }, (err, data) => {
       t.ok(err)
-      t.equal(err.code, 'HPE_INVALID_CONSTANT')
-      t.equal(err.message, 'Expected HTTP/')
+      t.type(err, errors.HTTPParserError)
     })
   })
 })