If you think about it, your IP is needed so that the packets can leave your network and return. If you run VPN software your IP still needs to be known but it could be an IP that is physically far away from you and in a different country. If that is all you want, then I am sure someone hear can recommend VPN software they trust.
If you need more anonymity then that you might consider the TOR Browser:
Protect your privacy and defend yourself against network surveillance and traffic analysis.
Defend yourself against tracking and surveillance. Circumvent censorship.
Which relies on Onion Routing. I have no experience with either system, I just know of their existence.