A system for controlling the tapping operation in which the turning of tap is effected by a digital spindle motor (1) in synchronism with the drive of tap in the axial direction by a servo motor (2) for tapping operation of high accuracy and high reliability. A speed instruction is supplied from a position control means (4) to a digital control circuit (5) which drives a spindle motor, the speed instruction being based upon a distribution pulse from an interpolation circuit (3a) which performs linear interpolation depending upon the pitch of a screw that is to be machined and upon a feedback signal that represents the rotational position of the spindle motor. The distribution pulse is further supplied to a servo circuit (12) for the servo motor from the interpolation circuit. Therefore, the two motors are driven in synchronism with each other. In one embodiment, the tapping operation is effected according to a fixed cycle in which the two motors are turned forward and reverse repeatedly to reciprocate the tap. In another embodiment, a switching means (7) to supply the distribution pulse and the feedback signal intermittently is provided in order to selectively perform the tapping operation.