Lundström's lawyer Per E Samuelsson told Sveriges Radio's P3 news programme on Monday that his client, who is a wealthy heir to the Wasa crispbread empire, accepts neither the criminal ruling nor the award of damages.
Lundström, along with Gottfrid Svartholm Warg, Peter Sunde and Fredrik Neij were convicted in April 2009 on charges of being accessories to copyright violations. they were sentenced to a year's imprisonment apiece and a combined fine of 30 million kronor ($4.4 million).
All four appealed their sentences, with the Svea court of Appeal ruling in November to uphold the convictions, with the exception of Svartholm Varg who was absent through sickness.
The appeals court however reduced Lundström's sentence to four months and increased the damages to a total of 46 million kronor.
On the opening day of the trial, Peter Sunde described the court proceedings as a "waste of time" as the case was inevitably destined for the Swedish Supreme Court.
Founded in 2003, The Pirate Bay, which claims to have more than 23 million users, makes it possible to skirt copyright fees and share music, film and computer game files using bit torrent technology, or peer-to-peer links offered on the site.