A knee air bag apparatus having a housing disposed in or adjoining a lower region of an instrument panel extending from front to rear having an outlet opening. An inflator and a knee air bag are mounted in the housing in the initial state, and in an expanded state deploys in front of the instrument panel. The air bag outer skin has a protective section and a fill and support section. The protective section when expanded state is positioned, in front of the instrument panel. To improve deployment behavior, the fill and support section features a vehicle-front section such that with the knee air bag fully expanded, the front section extends beyond the vehicle front end of the housing in the direction of the vehicle front.