Gustafsson was on trial, accused of killing his three friends on a camping trip to Lake Bodom near Helsinki, in 1960.
Gustafsson had said the group was attacked by an unknown assailant while sleeping in a tent.
In its decision, Espoo district court said that the long period of time since the commission of the crime had made it difficult to gain an accurate picture of events.
However, it added that eyewitness testimony from the morning after the murders supported the defence claim that there was an outsider at the site of the crime.
The prosecution re-opened the case last year with the help of new DNA evidence. It is widely expected that the case will go to a court of appeals. Prosecutors have a week to decide whether to appeal.