Tunstall councillor Lee Wanger was found guilty of encouraging the spread of internet child porn after logging on to a website under investigation.
He was fined £250 and placed on the sex offenders' register for five years at Derby Crown Court on Thursday.
Brian Ward from the Independent group says he may have to leave his position.
Wanger, from Ladywell Road, Tunstall, Stoke-on-Trent, was charged for logging on to a website which was being investigated by police, although officers failed to find any indecent images on his computer.
He was found guilty of incitement to distribute indecent photographs of children between 1 June and 31 July 1999.
Disgracefully, convicted paedophile and Deputy Leader of the Conservative and Independent Alliance Group in the city, Cllr Lee Wanger is allowed to nominate and vote in the school governor process even though he is on the sex offender's register.