An air bag for steering wheel of the invention is folded and housed in a boss positioned in the vicinity of the center of a ring of a steering wheel gripped by a driver during steering. The air bag includes a driver side wall and a wheel side wall that are substantially equal in outer shape to each other. The wheel side wall includes an opening for supplying an inflation gas therethrough in the center. A periphery of the opening provides an area for attachment of the air bag to the steering wheel. A thickness regulating tether for regulating the separation distance between the driver side and wheel side walls and thus regulating the thickness of the completely inflated air bag is disposed in the vicinity of the opening. An oscillation regulating tether for regulating the separation distance between the driver side and wheel side walls is disposed in the vicinity of the ring of the steering wheel in the completely inflated air bag. The separation distance between the walls which distance is regulated by the oscillation regulating tether is such a length that the air bag can secure a cushioning action, and is shorter than the separation distance between the walls regulated by the thickness regulating tether. The air bag enables the oscillation regulation tether to restrain oscillations from occurring in the course of inflation.