The description fits, but i'm nut quite sure... Whatever, tell me if it rings a bell...
There a movie called the Dead Next Door. It features a squad of zombie killers that discovers the existence of a religious cult that are for the zombies because they think the flesh eaters are godsent, here to destroy the sinned humans.
There's a scientist affiliated with that squad that creates a serum to make zombies humans. The problem is that it was injected to a member of the squad that was not quite dead, turning him into a not quite-zombie zombie. He's intelligent, but he still likes flesh, and wants the doctor dead.
The movie is from 1988, here is the zombie-human guy: