The 25-year-old man had been found not guilty at Attunda district court in Stockholm in the first case of its kind since the law came into force in April.
He had been accused of trying to travel to Syria to join the Jihadi group Jabhat al-Nusra.
The man, who lives in Södertälje, west of Stockholm, was stopped by Turkish police at Istanbul Airport in April, less than two weeks after the new law came into force.
According to Dagens Nyheter the man was on a one way ticket and in his bag was a bulletproof vest, camouflage uniform and kneepads. He had also searched for Jabhat al-Nusra on his phone, the newspaper reported.
After he was questioned by Turkish police, Swedish security services were contacted and the man was flown back to Sweden, DN reported.
The man denies that he was travelling to Syria to join a terrorist group. His lawyer said his intention was to take part in humanitarian work.
At his original trial, the court said the prosecutor had not proved the suspect would have been able to reach the area in Syria controlled by Jabhat al-Nusra and, even if he had, that he would have been allowed to join the organisation.
For that reason, the court decided to declare the man not guilty of the charges.
The prosecutor appealed and the case is being heard again in court on Tuesday.
The Secretary General of the Swedish Bar Association, Anne Ramberg, told Radio Sweden they had concerns when the law was first proposed.
"The problems are still there," she said. "The prosecutor has the burden to prove that the idea with the trip was to go down and fight and, as the Swedish Bar Association together with others advocated when giving our opinion, it was obvious that it would be very difficult to apply.
"What is criminalised is very much in the head of the person."