Ashfield District Council in Nottinghamshire cancelled the show as it felt the comedian's material was not "appropriate".
Ricky-Lee Cooke, who started a petition to overturn the decision, said people had the right to make their own choice.
Brown's manager accused the council of a "vendetta" against his client.
The authority said the comic was free to perform at a non-council venue.
Roy "Chubby" Brown was due to appear at Festival Hall, in Kirkby, in October.
Mr Cooke, whose petition has 465 signatures, said: "I'm a big believer in freedom of speech... I do believe it's censorship.
"It's for the people to decide, no one is forcing [them] to go. They know what the show is like.
"I do think [the material] is appropriate and I don't think the council should be making decisions like this."
Roy "Chubby" Brown is known for his so-called "blue" style of humour with some critics saying his act is "crude".
He rarely appears on mainstream television but did star in the TV programme the League of Gentleman as mayor of the fictional town, Royston Vasey - the comedian's real name.
Steven Lloyd, the comedian's manager, said: "We do shows for the fans, not for the council. This is purely a vendetta against Roy as they have not banned other comics from the venue.
"They booked the show last November and it took them [until] now to cancel it because they didn't want 'his type'."
He added that the comic felt "badly treated".
The council said in a statement: "In discussions about the provisional booking, a decision was taken not to go ahead.
"The booking was not confirmed, and tickets were not put on sale. There is no financial loss or missed income for Ashfield District Council."
In a previous statement it said it did not feel the booking was "appropriate for a council venue and not one that it wished to be associated with."
Hundreds of people have called for a council to lift a ban on the comedian Roy "Chubby" Brown appearing at one of its venues.