An active vibration damper for a reciprocating machine part, comprising an inertial mass that can be displaced in the direction of the reciprocating motion and a support plate that can be fastened to the machine part. The inertial mass and the support plate are connected to one another by a spring element. The natural frequency of the vibrating system constituted by the inertial mass and the spring element is at most as great as the frequency of the reciprocating motion. The inertial mass can be moved by plunger coil fastened to the support plate so as to be immobile with respect thereto, and the spring element can be deformed by the plunger coil. The inertial mass consists of a cup-shaped magnet that at least partly concentrically surrounds the plunger coil radially on the inside and outside. The cup-shaped magnet is guided by a guideway parallel to the axis of the plunger coil.