A control device includes a speed setting unit configured to set a relative movement speed of a wire electrode with respect to a workpiece depending on the average of gap voltage per unit time, i.e., average gap voltage, and set the relative movement speed so as to move the wire electrode backward when the average gap voltage is less than a threshold, and a map compensation unit configured to change the threshold from a first threshold that is set when the amount of change in the average gap voltage is lower than a predetermined variation, to a second threshold that is greater than the first threshold, when the average gap voltage has changed in a decreasing direction and the amount of change in the average gap voltage becomes equal to or greater than the predetermined variation.