To provide a new method of suppressing and controlling the torsional vibration of the shaft of a rolling mill, by which the torsional vibration of the shaft, which is caused when imparting speed variation to a motor, is effectively suppressed and the motor is made to be highly responsible.

By assuming that the motor 1, the rolls 2 of the rolling mill and a power transferring means between them are two inertia and by a driving system which includes an ideal motor speed model (motor speed compensator 11) taking the two inertia into consideration and an ideal torque model (torque compensator 10) taking the two inertia into consideration, the ideal motor speed and the ideal torque command at which the roll speed when a speed variation command is imparted to the motor 1 becomes an ideal responsive waveform which is free from the torsional vibration are calculated backward and the motor speed is controlled on the basis of these values.