A curtain airbag of a vehicle is provided adjacent to the roof of the vehicle in a folded state, is configured to have a shape that unfolds downward between an inner side surface of the vehicle and an occupant when the vehicle crashes, and includes an outer panel that proceeds toward the side surface of the vehicle and an inner panel that proceeds toward the occupant upon expansion. The curtain airbag further includes a head support part configured to have a shape in which an expansion thickness, which is defined by the outer panel and the inner panel in a portion that the head of the occupant contacts due to the car crash, gradually increases toward the front of the vehicle, so as to prevent the head of the occupant from rotating while moving toward the front of the vehicle. The curtain airbag may effectively stop the head of the occupant from rotating while moving toward the front of the vehicle during a vehicle crash.