A torsional damper pulley improved in general versatility, easily produced and capable of reduction in production cost. The torsional damper pulley is constructed of a hub 11 fixed at a revolving shaft of an internal combustion engine, an annular pulley body 10 coaxially placed at an annular fixing portion 11b at an outer circumference of the hub, and an elastic solid 13 interposed between an outer circumferential surface of an annular fixing portion and an inner circumferential surface of the pulley body. The pulley body 10 is constructed of an annular frame 12 substantially U-shaped in section, having an concave portion 15 open at one side in an axial direction, and an inertia mass element 14 inserted into the concave portion 15 in an axial direction and fixed. The inertia mass element is a laminate made by overlaying annular plates 14a on each other and bonding them, and the inertia mass element is fixed by being press-fitted into the concave portion.