Williamson, 71, who was not in court, had appealed his conviction by a court in Regensburg, southern Germany, for denying key facts about the Holocaust in an interview he gave to Swedish television in Regensburg in 2008.
The bishop alleged he was duped by a Swedish reporter into believing the interview would only be broadcast in Sweden.
Lawyers for London-based Williamson did not deny the statements made by the bishop, a member of the breakaway ultra-conservative Catholic fraternity the Saint Pius X Society, but stressed that in Sweden such opinions could be freely voiced.
In Germany it is an offence to deny that the Nazis murdered six million Jews during World War II.
Williamson told Swedish television that "200,000 to 300,000 Jews perished in Nazi concentration camps" and disputed the existence of the gas chambers.
In April 2010, Williamson, who now lives in London, was fined €10,000 by the lower court, reduced from an earlier fine of €12,000 he had refused to pay, for inciting racial hatred.