diff --git a/lib/Connection.js b/lib/Connection.js
index 88a154ae6..feaa3ab23 100644
--- a/lib/Connection.js
+++ b/lib/Connection.js
@@ -113,7 +113,14 @@ class Connection {
     const onError = err => {
       cleanListeners()
       this._openRequests--
-      callback(new ConnectionError(err.message), null)
+      let message = err.message
+      if (err.code === 'ECONNRESET') {
+        /* istanbul ignore next */
+        const socket = request.socket || {}
+        /* istanbul ignore next */
+        message += ` - Local: ${socket.localAddress || 'unknown'}:${socket.localPort || 'unknown'}, Remote: ${socket.remoteAddress || 'unknown'}:${socket.remotePort || 'unknown'}`
+      }
+      callback(new ConnectionError(message), null)
     }
 
     const onAbort = () => {
diff --git a/test/unit/connection.test.js b/test/unit/connection.test.js
index 5ba1c494a..a556564a0 100644
--- a/test/unit/connection.test.js
+++ b/test/unit/connection.test.js
@@ -1084,3 +1084,25 @@ test('getIssuerCertificate detects invalid/malformed certificates', t => {
   }
   t.equal(getIssuerCertificate(socket), null)
 })
+
+test('Should show local/remote socket address in case of ECONNRESET', t => {
+  t.plan(2)
+
+  function handler (req, res) {
+    res.destroy()
+  }
+
+  buildServer(handler, ({ port }, server) => {
+    const connection = new Connection({
+      url: new URL(`http://localhost:${port}`)
+    })
+    connection.request({
+      path: '/hello',
+      method: 'GET'
+    }, (err, res) => {
+      t.ok(err instanceof ConnectionError)
+      t.match(err.message, /socket\shang\sup\s-\sLocal:\s127.0.0.1:\d+,\sRemote:\s127.0.0.1:\d+/)
+      server.stop()
+    })
+  })
+})