Napster requested the hearing in February, after the US Court of Appeals for the 9th Circuit in San Francisco ruled that the company had infringed copyright laws.
District court judge Marilyn Hall Patel slapped an injunction on the company in March, preventing it from allowing its users to swap copyrighted music files.
Napster complied by introducing software to try and prevent access to the offending files and, since then, Napster's user numbers have dropped dramatically.
A group of the world's biggest record companies, including Vivendi Universal Music, Sony Music, EMI and Bertelsmann, sued Napster in December 1999 for copyright infringement. If the case eventually goes to a full trial, Napster could owe the record companies millions of dollars in damages, more than it is worth according to some experts.
Napster could still make one final appeal -- this time to the US Supreme Court.
In the meantime, the company is working on a subscription-based model, which it hopes to launch by the end of the summer.