Peter Mangs was sentenced in 2012 to life in prison after he was convicted of two murders and five attempted murders in the southern city of Malmo, the news agency TT reported.
Mangs, dubbed a "serial sniper," had been charged with 12 attempted murders after police said he shot at homes, businesses and cars and out in the open with a Glock 19 pistol.
He seriously injured numerous people, leaving many of them close to death, police said.
At his November trial, Mangs also was convicted of vandalism, violent assault and perverting the course of justice.
One judge said Mangs should only be convicted of one murder.
Mangs was acquitted of a third murder, five attempted murders, conspiracy to commit murder and several other charges.