A control apparatus of a machine tool comprising: workpiece holding means for holding a workpiece; a tool rest to hold a cutting tool that cuts the workpiece; feeding means (150, 160) for feeding the cutting tool toward the workpiece in a predetermined feeding direction via relative movement between the workpiece holding means and the tool rest; rotating means for causing relative rotation between the workpiece and the cutting tool; and vibration means for causing relative reciprocal vibration between the workpiece holding means and the tool rest andmaking a cutting portion during forward movement of the vibration overlap with a cutting portion during backward movement of the reciprocal vibration, what means that a portion of a circumferential surface of the workpiece that is cut during a n+1th rotation includes a portion of the circumferential surface of the workpiece that has already been cut during a nth rotation, the machine tool being capable of cutting the workpiece via the relative rotation between the workpiece and the cutting tool and via the feeding of the cutting tool toward the workpiece with the reciprocal vibration in the feeding direction, wherein the control apparatus comprises vibration frequency setting means for setting vibration frequency of the reciprocal vibration with respect to one relative rotation when machining the workpiece so that intersections (CRs) of paths of the cutting tool during the forward movement and the backward movement are dispersed on a circumferential surface of the workpiece, i.e. that an intersection between a path of the cutting tool in the nth rotation and a path of the cutting tool in the n+1th rotation and an intersection between a path of the cutting tool in the n+2nd rotation and a path of the cutting tool in the n+3rd rotation are located out of alignment with each other in the direction of the relative rotation, characterised in that the vibration frequency setting means sets the vibration frequency on the basis of the difference between a maximum value and a minimum value of roughness of a machined surface of the workpiece or on the basis of the maximum value. workpiece holding means for holding a workpiece; a tool rest to hold a cutting tool that cuts the workpiece; feeding means (150, 160) for feeding the cutting tool toward the workpiece in a predetermined feeding direction via relative movement between the workpiece holding means and the tool rest; rotating means for causing relative rotation between the workpiece and the cutting tool; and vibration means for causing relative reciprocal vibration between the workpiece holding means and the tool rest andmaking a cutting portion during forward movement of the vibration overlap with a cutting portion during backward movement of the reciprocal vibration, what means that a portion of a circumferential surface of the workpiece that is cut during a n+1th rotation includes a portion of the circumferential surface of the workpiece that has already been cut during a nth rotation, the machine tool being capable of cutting the workpiece via the relative rotation between the workpiece and the cutting tool and via the feeding of the cutting tool toward the workpiece with the reciprocal vibration in the feeding direction, wherein the control apparatus comprises vibration frequency setting means for setting vibration frequency of the reciprocal vibration with respect to one relative rotation when machining the workpiece so that intersections (CRs) of paths of the cutting tool during the forward movement and the backward movement are dispersed on a circumferential surface of the workpiece, i.e. that an intersection between a path of the cutting tool in the nth rotation and a path of the cutting tool in the n+1th rotation and an intersection between a path of the cutting tool in the n+2nd rotation and a path of the cutting tool in the n+3rd rotation are located out of alignment with each other in the direction of the relative rotation, characterised in that the vibration frequency setting means sets the vibration frequency on the basis of the difference between a maximum value and a minimum value of roughness of a machined surface of the workpiece or on the basis of the maximum value.