The four men behind the site said they would not pay the fine.
A Swedish court has thrown out a request for a retrial by the four men behind The Pirate Bay website.
The four were found guilty of promoting copyright infringement in April and face jail sentences and hefty claims for damages.
The Pirate Bay's lawyers called for a retrial when it emerged that one of the judges in the case belonged to several copyright protection groups.
The Swedish court said the judge's affiliations did not bias the case.
The Svea Court of Appeal said Judge Tomas Norstrom should have declared that he was a member of the Swedish Association for the Protection of Industrial Property and the Swedish Copyright Association before the case went to trial.
"The fact that he failed to shed light on this does not however mean that there was any wrongdoing during the proceedings that would require a retrial," said the court in a statement.
"This was not a case of bias," concluded the court.
No appeal is allowed against the judgement.
The Pirate Bay is well-known for hosting lists of links that give people access to pirated copies of movies, music, software and TV shows.
The Pirate Bay defended itself saying that it did not infringe copyright because none of the pirated material is stored on its servers.
The court found them guilty because, it said, they continued to operate the service even when they knew users were being pointed to pirated material.
The four men behind The Pirate Bay, Frederik Neij, Gottfrid Svartholm Warg, Carl Lundstrom and Peter Sunde, were sentenced to one year in jail and told to pay damages of 30m Swedish kronor (£2.3m, 2.7m euros) to entertainment companies such as Warner Bros and Sony Music Entertainment.
In response to the ruling Peter Sunde said The Pirate Bay would now file charges against Sweden for violating the human rights of the defendants.