A damping apparatus for an automobile is provided, capable of ensuring a high level of reliability while obtaining excellent damping effect with simple configuration. The damping apparatus for an automobile that reduces vibrations of an automobile body may include an actuator that is attached to the automobile body and drives an auxiliary mass; a current detector that detects a current flowing through an armature of the actuator; a section that detects a terminal voltage applied to the actuator; a calculation circuit that calculates an induced voltage of the actuator, and further calculates at least one of the relative velocity, relative displacement, and relative acceleration of the actuator, based on a current detected by the current detector and the terminal voltage; and a control circuit that drive-controls the actuator based on at least one of the relative velocity, relative displacement, and relative acceleration of the actuator calculated by the calculation circuit.