Brian was killed in the 'Life of Brian' episode of the show, which aired on November 24, said the Hollywood Reporter.
In the episode, the dog gets struck by a car and dies because of the injuries, which makes Griffins adopt a new pet.
Since it was created on November 25, the petition has collected more than 19,000 signatures.
Petition organiser Aaron Thompson said, "Brian Griffin was an important part of our viewing experience. He added a witty and sophisticated element to the show. Family Guy and Fox Broadcasting will lose viewers if Brian Griffin is not brought back to the show."
Explaining their decision to kill off the character which had been on the show since its debut in 1999, executive producer Steve Callaghan had said to E! Online, "We thought it could be a fun way to shake things up."
"Our fans are smart enough and have been loyal to our show for long enough to know that they can trust us. We always make choices that always work to the greatest benefit of the series.
