A torque command supplied to a tape running unit for drawing out and driving a tape wound on a first reel is modulated by a torque modulator depending on a moment of inertia of the first reel, a winding radius of the tape wound on the first reel, a moment of inertia and a rotating radius of the tape running unit, 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.