In this paper, a novel torsional vibration predictive control design based on DMC (dynamic matrix control) is proposed for drive system. The state equation of two-mass drive system is established based on model matching. A PI-DMC controller for suppressing torsional vibration of drive system was designed by PI controller with dynamic matrix control. The random disturbance is avoided by inner-controller, and the external-controller can improve control precision and dynamic response of drive system. The effectiveness and usefulness of the proposed schemes are verified with the simulation. The simulation results show that the control method can suppress torsional vibration effectively, and improve transmission performance of drive system.