To damp vibration based on a torque fluctuation of a driving system for a vehicle with a reciprocating piston engine by using the torque of torque applying means such as a motor or a generator connected to the driving system while considering the behavior of the vehicle and an output property of the engine.

The waveform of a torque fluctuation arising in the driving system depending on the operated condition of the engine is estimated, and vibration damping load torque or vibration damping driving torque in the direction of canceling the same is applied to the driving system by using the torque applying means such as the motor or the generator while checking whether the behavior of the vehicle reaches a predetermined limit or not and checking the output property of the engine.