A cable tension control device includes a pair of first active rollers clamping a cable therebetween, a first driver driving the first active rollers, a pair of second active rollers clamping the cable therebetween at an upstream position from the first active rollers, a second driver driving the second active rollers, a floating roller arranged between the first active rollers and the second active rollers and exerting a pushing force on the cable, and an actuator driving the floating roller to move vertically to adjust the pushing force exerted on the cable. A tension force applied on the cable is controlled to be equal to a predetermined tension force by controlling the pushing force and by controlling a speed difference between a first speed at which the first active rollers convey the cable forward and a second speed at which the second active rollers convey the cable forward.