A torsional vibration damper that can reduce collision noise of an inertia body when a rotary member is stopped, and a control device therefore. In the torsional vibration damper, a rotary member is mounted on an output shaft of an engine such that none of rolling masses is situated within a predetermined angle range above a rotational center axis of the rotary member when the engine is stopped. Therefore, when the engine is stopped, the inertia body will not be supported by only one of the rolling masses situated within the predetermined angle range.