The work aims to develop an active control method for mitigating torsional vibration of a rotating mechanical system with a rigid coupling, driven by an electric motor, in order to achieve good tracking and disturbance rejection performances. It is commonly known that torsional oscillations in a rotating system, which is normally used for various power transmission systems, can generate a significant level of vibration. In this work, therefore, an active control system that was based on the Active Disturbance Rejection Control (ADRC) approach was utilized to develop the control system that was robust against uncertainties associated with the internal dynamics and external disturbances affecting the system. The Extended State Observer (ESO) was used to estimate the generalized disturbance consisting of not only the external disturbances but also the disturbances associated with internal dynamics of the rotating system. The effectiveness of the developed control system was demonstrated, which showed that in the case of the varying coupling and load inertias, the control system could still perform well.