If you remember then you might know that Google has already launched a URL shortening service, Goo.Gl, which is now publicly access and anyone can use it,

Now Google has launched another URL shortening service name as G.Co, actually this service will be used to shorten only URL containing Google Pages, means you cant use it shorten URL of your favorite websites,

Google says :-

In the world of URLs, bigger is not always better. In 2009, we helped shrink up long, unwieldy URLs by launching our public URL shortener, goo.gl. Today, we’re announcing a new URL shortcut that will only link to official Google products and services: g.co.

The shorter a URL, the easier it is to share and remember. The downside is, you often can’t tell what website you’re going to be redirected to. We’ll only use g.co to send you to webpages that are owned by Google, and only we can create g.co shortcuts. That means you can visit a g.co shortcut confident you will always end up at a page for a Google product or service.

There’s no need to fret about the fate of goo.gl; we like it as much as you do, and nothing is changing on that front. It will continue to be our public URL shortener that anybody can use to shorten URLs across the web.

Currently if you try to open G.Co then you will see page like below :-