The sign was put up at the same time the store, formerly owned by Smile, was sold to Martin McColl.
Local historians have campaigned fiercely to retain the Victorian facade of the high street and claim that the Booze Busters sign "sticks out like a sore thumb", while residents have said that it gives a bad impression of the high street and are pressing for the sign to be ripped down.
Local councillor Reyna Knight said that she had received a number of complaints from Portishead residents and would be checking that planning regulations had been complied with. "I have taken up the matter with the planning department," she said.
She also criticised the retailer's promotion of discount alcohol. "With the police having done such a lot of work to reduce alcohol-fuelled anti-social behaviour, advertising discount alcohol in this way is somewhat irresponsible."
Just days after the Booze Busters sign was put up, the local off licence changed its name to Discount Booze, sparking more furore.
Martin McColl declined to comment on the claims about the promotion of discount alcohol, but said that it would install the Booze Busters fascia only within planning guidelines.