In the machine tools, low frequency vibration, which is called rocking vibration has a great influence on the tool-workpiece vibration. In this paper, to reduce the rocking vibration, a new damping systems is proposed to increase the damping of support system without decreasing the stiffness of support. This support system is based on stiffness tuning technique proposed in the previous study. An experiment is conducted to verify the effect of the proposed damper system. As a result, the proposed damper increases the damping of support system without decreasing the stiffness in an appropriate range of damper preload.