A steering wheel having an air bag device which includes a ring portion, a boss portion, a bracket, a spoke and an air bag device. The boss portion has a boss and a boss plate extending laterally from the boss periphery. A bracket made of plastically deformable metal has a supporting portion inclined outwardly in opposite directions toward the ring portion. The air bag device is held at a predetermined distance from the boss plate by the bracket and includes a bag holder made of plastically deformable metal and having connecting portions inclined at the same angle as the supporting portions of the bracket. By providing supporting portions inclined in opposite directions, the steering wheel of the present invention can absorb impact energy not only by inflation of the air bag device but also by deformation of the supporting portions due to rotation of the air bag device during impact.