We have developed the novel device that can extract energy from ocean waves utilizing the heaving motion of a floating mass. The major components of the energy converter are: a floater, a counterweight, a cable, a driving pulley, two idler pulleys, a ratchet, and a generator. The device generates power through the tension force in the cable and the weight difference between the floater and the counterweight. When the system is at static free condition, the tension in the cable is equal to the weight of the counterweight which is minimum. Therefore it is desirable to keep the counterweight lighter than the floater. However, experiments show that during the rise of the water level, the torque generated by weight of the counterweight is insufficient to rotate the driving pulley which causes the cable on the floater side to slack. The proposed application of the tension pulley rectifies these problems by preventing the cable from becoming slack when the water level rises. In this paper, the dynamics model is modified to incorporate the dynamics of the tension pulley. This has been achieved by first writing the dynamical equations for the tension pulley and the energy converter separately and combining them later. This paper investigates numerically the effect of the tension pulley on various physical quantities such as the cable tension, the floater displacement, and the floater velocity. Results obtained indicate that this application is successful in suppressing large fluctuations of the cable tension.