In this paper, the new robust torsional vibration suppression control scheme is proposed for the two mass system. A reduced order state feedback controller where the motor speed and the observed torsional torque are fed back and the PI controller are proposed as the torsional vibration suppression controller. Using the estimated mechanical parameters by off-line RLS(Recursive Least Square) algorithms, the speed controller for torsional vibration suppression is designed and its gains are determined using the Kharitonov robust control theory. The Kharitonov robust control theory can obtain the robust stability with a specified stability margin and a damping limit and the good performance of vibration suppression although if the parameters are varied within some specified limit. The effectiveness and usefulness of the proposed schemes are verified with the simulation and the experimental results on the fully-digitalized 5.5kW two mass system.