A wire tension control device mounted on the wire cutting electric discharge machine and capable of accurately controlling the wire tension. The device is provided with a wire tension detecting mechanism (70) supported by a slider (72) displaceable relative to the machine proper and having a displacement roller (73) displaceable jointly with said slider. A control unit (90), which receives output signals representing an actual displaced position of a displaceable roller from a linear sensor (80) measuring in a non-contact manner the distance between the displaceable roller and a reflecting mirror on the slider by the use of laser beams, supplies, to a powder clutch (60), excited electric current corresponding to a value obtained by deducting the actual value of sensor output signal corresponding to a set value of wire tension. A clutch applies a set degree of tension to the wire (50) while exerting braking force varying according to an actual wire tension upon the braking roller (44).