This paper presents the optimal energy management scheme for island microgrid applications with direct-drive wave energy converter (DDWEC) and hybrid energy storage system (HESS). Because the motion of the wave is irregular, resulting in frequent and violent changes in the power captured by the generator. HESS plays a very vital role in smoothing out such fluctuations and maintaining a stable DC bus voltage. This paper reduces the times of battery charging and discharging by Optimal Energy Management Scheme (OEMS) to extend its service life. Two-loop control is used where the outer loop controls the DC bus voltage stabilization and the inner loop uses MPC (Model predictive control). MPC helps to handle sudden changes in power generation and load power demand. HESS is used to compensate the difference in average and instantaneous power between the wave generation system and the DC load. MPC aims to regulate the battery and supercapacitor (SC) currents to track the dynamic current reference. The proposed optimal energy management scheme and control structure are verified by simulation results.