The trial, which is being held in Gostrup, Denmark, was heavily guarded by police as journalists from Swedish and Danish media gathered outside the court.
The four men have been in custody for more than a year after they were arrested in December 2010. All the defendents maintained their innocence prior to the start of the trial.
"This is a serious terrorism case, perhaps more serious than all other terrorism cases we have had, as the arrests were made closer to the planned attack," the Danish prosecutor presiding over the case, Gyrithe Ulrich, told Swedish Radio News.
According to the Danish security police, PET, the defendants planned to force their way into Jyllands-Posten's editorial offices in central Copenhagen and kill as many people as possible.
The defendants' arrest was a result of cooperation between the Danish security police and Säpo, the Swedish intelligence service.
Phone surveillance carried out by the Swedish intelligence service in Järfälla outside Stockholm, where one of the defendants lives, provided information that allowed the Danish security police to arrest the four men the morning after the crossed the Öresund bridge to Denmark on 28 December 2010.
In September 2005, Jyllands-Posten published cartoons depicting the Muslim prophet Muhammad, prompting widespread and violent protests in many Islamic countries.