The perpetual oscillations of ocean waves produce potential energy, which can be converted to electrical energy with the help of direct drive linear generators. The fluctuating generated power poses a major challenge when it is supplied to the power grid. In this paper, a supercapacitor provides the short-term energy storage to buffer and smooth out the power fluctuations. A new coupled model of a wave energy converter and a linear generator is proposed for its response characterization under varying system conditions. The developed model and an advanced control strategy is used to exhibit a smooth and stable operation of the wave-to-wire system. The generator side converter is controlled to extract the maximum power from the waves and to minimize the generator losses by controlling its d-axis and q-axis currents. The grid side converter is controlled to keep the dc-link voltage constant and to generate the required voltage waveforms at the point of common coupling. The performance of the proposed control strategy for the wave-to-wire system is investigated under different applied diffraction forces. The simulation results show that with the use of proposed control scheme and the supercapacitor, the wave-to-wire system can operate in a smooth and stable operation under normal and fault conditions.