In recent years, a force control system is applied to many applications. There is much reseache about force control for machine tools. Generally, in force control systems, the force infomation from the environment is detected by force sensor. However, the control system using force sensor has some problems, such as signal noise, colocation problem and narrow bandwidth. This paper proposes a new force sensor-less control system using a reaction torque observer. The proposed control method is applied to a machine tool using ball screw. Since the actuator using ball screw and timing belt has a torsional vibration phenomenon, the proposed reaction torque observer should consider this torsional vibration. As a result, this paper realizes the sensor-less control for machine tool using reaction torque observer. The validity of the proposed force control method is confirmed by several experimental results.