An apparatus which moves a tool back and forth in synchronism with rotation of a workpiece with respect to the workpiece to machine the workpiece into a non-circular shape. The tool is attached to a tool mount placed on a tool mount table which is connected to be moved in a direction perpendicular to the axis of a spindle by a motor. The tool is connected to be moved in a direction perpendicular to the axis of the spindle with respect to the tool mount by a high speed actuator. Profile generating movement of the tool is thus provided by a combination of movement provided by the motor and movement provided by the high speed actuator. The high speed actuator is controlled in accordance with high frequency components included in profile data while the motor is driven in accordance with low frequency components included in the profile data. As a result, the responsiveness in profile generating movement of the tool is improved, and high speed machining of a non-circular workpiece is enabled.