PROBLEM TO BE SOLVED: To suppress speed change and large displacement of a dancer arm, stabilize tension control and prevent collision of the dancer arm to a stopper upon a rapid reduction in web tension in a tension application device.SOLUTION: In a tension application device 2 in which a web (wire 7) is wound over a dancer roller 5 of a movable dancer arm 4 and target tension is applied to the running web (7) through driving the dancer arm 4 by an actuator (torque motor 6, linear motor 61), the speed V or the position P of the dancer arm 4 is detected during the running of the web (7); a correction signal e based on the speed V or the position P is fed back to a command signal a when Speed V becomes equal to or larger than Upper Limit Speed V1 or Position P becomes equal to or larger than Correction Position P1 as the tension of the web (7) is reduced rapidly, and the speed of the actuator (6, 61) is reduced by (Command Signal a-Correction Signal e).