An air bag apparatus for protecting a passenger's head includes an air bag cover fixedly installed at an upper end of a seat back and an air bag cushion installed in a folded state in the air bag cover. The air bag cushion is deployed while breaking the air bag cover during supply of air bag gas from an inflator, and deployed toward one side of the passenger who is on a seat to protect the passenger's head during deployment. Accordingly, the air bag apparatus protects the passenger's head even in a situation in which a position of the seat is changed and an autonomous driving condition in which various sitting modes are arranged.