Persbrandt, a household name in Sweden, had a supporting role in The Hobbit: The Desolation of Smaug as the shapeshifter Beorn who gives the dwarves and the hobbit shelter.
On Tuesday he was found guilty of and sentenced for buying 12 grammes of cocaine, the Aftonbladet newspaper reported.
His alleged dealer was one of eleven people in a complicated narcotics case. Persbrandt, 50, has always maintained his innocence and said he did not know why his number was among the dealer's phone contacts.
"If it turns out an order was made, it was another person who used his phone," lawyer Per Liljekvist told Aftonbladet earlier this year. He maintained that Persbrandt had been at a party on the evening in question, and that he often let his mobile phone lie about.
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Liljekvist has now, just two hours after the verdict and sentencing were made public, appealed on behalf of his client. The jail sentence would come into effect when the appeals court either decides not to take on the case, or, if it it takes it on, if upholds the lower court's verdict and punishment.
The prosecutor said he was convinced that if the case reached the appeals court, it would reach the same verdict as the district court.
"I think there is sound evidence and it was a sound investigation," Lars Ågren told Aftonbladet.