A reward of £2,000 is being offered by McDonald's after several of its outlets in Weston-super-Mare were targeted by criminals.
A spokeswoman for the hamburger chain said the police believe a group calling itself Neo Anarchy is responsible.
She said criminals caused "substantial" damage to the three outlets in the town in a series of attacks during 2004.
Avon and Somerset Police have launched an investigation into the attacks which took place last year.
"Damage has been very disruptive. Police have told us a group calling itself Neo Anarchy may be responsible for the attacks," the spokeswoman said.
The reward is being offered for information leading to the arrest and conviction of those responsible for the damage.