The invention discloses a constant tension control device and a control method. The constant tension control device comprises a first guide wheel, a floating pulley assembly, a second guide wheel, a measuring and monitoring mechanism, a guide wheel mounting plate, a third guide wheel, a bottom plate, a driving mechanism and an encoder; one end of a base material is attached to a winding roller ina winding manner, and the other end of the base material sequentially penetrates through the third guide wheel, the measuring and monitoring mechanism, the second guide wheel, the floating pulley assembly and the first guide wheel from the winding roller; and the driving mechanism is used for driving the winding roller to rotate according to a tension value, displayed by the measuring and monitoring mechanism, of the base material, so that winding or unwinding of the base material is achieved, and the tension of the base material is kept constant. According to the constant tension control device, a motor-driven magnetic powder clutch is used as an actuating mechanism, and the floating pulley assembly is used for passive adjustment, so that the tension of a controlled target is well controlled; and the tension of the controlled target is accurately controlled by adopting a method of combining feedforward control and feedback control, so that the control precision is improved.