Torsional vibrations present in the drive train can produce large stresses on the components of the wind turbine. Those torsional vibrations can be excited by either turbulent winds or grid disturbances which are considered in this study. A damping system accomplished by the decoupled power control for rotor side converter equipped with a torsional damper is developed. During vibrations, the torsional damper extracts the ripple of the generator speed to produce an auxiliary active power reference, which enables the system to generate additional active power to damp the drive train vibrations. To illustrate the effectiveness of the torsional damper, eigenvalue analysis is conducted through small-signal stability model and Bode diagram of the closed loop system is plotted. Simulations are performed in Matlab/Simulink to evaluate the proposed damping method. Results confirm that the torsional damper can introduce an auxiliary damping to the wind turbine system and exhibit a good performance to damp both vibration frequencies of the drive train, particularly the low frequency mode.