The authors present a novel control method to suppress the torsional vibration of a flexible joint which connects the motor shaft and the driven link. To obtain the stability against the torsional vibration, it is necessary to insert an artificial damper element to some extent in the control law. Estimated link velocity is fed back for damping. This link velocity is estimated by an observer without using any sensor for the link portion. For the purpose of the estimation, an acceleration controller which is realized by a disturbance observer, is applied. The experimental results are shown to verify the proposed method.