A magnetic braking apparatus (301) is integrally attached with a load detector (17, 303) such as an arm-like load cell through an attachment member, an outer fin, or a rotary joint between a yoke body (201) and a stationary portion of an outside construction or facility thereby to form a magnetic braking apparatus having a function of load detection. A tension control system incorporates the magnetic braking apparatus with the load detector (17, 303) attached thereto to apply a braking force to a let-off reel. A controller (304) in the tension control system calculates a roll diameter (D) of the let-off reel based on a number of rotations detected by a rotation detector (102) and a number of pulses generated in one rotation of the let-off reel, and generates a control signal representative of a desired braking torque which corresponds to the calculated roll diameter. The controller (304) further receives from the load detector (17, 303) of the magnetic baking apparatus, a feedback signal representative of an actual braking force applied to the let-off reel, and the controller (304) calculates an error signal between the desired braking torque signal and the feedback signal. The error signal is applied to the magnetic braking apparatus (301) to excite the same. Thus, the accuracy of tension control is improved. When a mechanical loss compensation signal is applied to the controller (304) to generates the control signal representative of the desired braking torque by taking the mechanical loss compensation signal into consideration, the influence of the mechanical loss can be removed.