An airbag apparatus for a front passenger's seat is disclosed. The apparatus includes a wrapping member that wraps up an airbag in a folded-up configuration. The wrapping member includes a joint portion that is secured to an airbag housing or its vicinity together with the airbag, a main body that extends forward from the joint portion and a cover portion that extends rearward from the joint portion for deployment between the airbag and an out-of-position object in an initial phase of airbag deployment. During a folding process of the airbag, the cover portion is wrapped around a front-rear contracted bag, and a leading end of the cover portion is tucked down between an upper folded portion and a lower folded portion of the front-rear contracted bag.