A torque command is applied to a tape running unit. The tape running unit for draws out and drives a tape wound on a first reel and taken up on a second reel. The torque command is modulated by a torque modulator in accordance with a moment of inertia of the first reel, a winding radius of the tape wound on the first reel, a moment of inertia of the second reel and a rotating radius of the second reel, which are detected by a parameter detector. The first motor is responsive to the modulated torque command for rotating the first reel, thereby keeping the tension of the tape constant.