According to what we understand about gravity at the moment, anti-gravity isn’t possible unfortunately 🙁
However, we still don’t really understand how gravity works as a force. All of the other ‘forces’ have opposites – magnetic force, in a bar magnet for instance, has north and south poles. We’ve never discovered an opposite force of gravity! It’s all thought to be down to the fact that mass is what gives things gravity, and why heavier things have more gravity. The Higg’s boson that they reckon they found at the Large Hadron Collider is thought to be a big part in understanding this.
Who knows, one day when we understand more about how gravity actually works, we’ll all be flying around with anti-gravity jetpacks!