The fires were started on consecutive Sundays in October in the Chatsworth area of Los Angeles, the Los Angeles Daily News reported.
Investigators have released surveillance video of the suspect taken early Oct. 28.
Most of the fires were started by someone igniting trash but there also were two car fires, officials said. Eight of the fires were reported Oct. 21 and the other four were Oct. 28.
Police asked that anyone with information on the suspect to call 213-893-9850.