The offer is for new customers wishing to access the service via a PlayStation 3.
The library has seven million tracks for you to stream and also has a MusicSync cloud feature that allows you to access tracks in your collection from Sony's cloud of tunes.
To access the free trial, log on to your PlayStation 3 and click on the Music Unlimited service below the Music icon.
Once the application has downloaded, follow the sign up instructions.
Sony recently announced a Music Unlimited app for Android smartphones, allowing you to stream music to your mobile.