The hybrid renewable energy system is a promising and significant technology for clean and sustainable island power supply. Among the abundant ocean energy sources, tidal current energy appears to be very valuable due to its excellent predictability and stability, particularly compared with the intermittent wind and solar energy. In this paper, an island hybrid energy microgrid composed of photovoltaic, wind, tidal current, battery and diesel is constructed according to the actual energy sources. A sizing optimization method based on improved multi-objective grey wolf optimizer (IMOGWO) is presented to optimize the hybrid energy system. The proposed method is applied to determine the optimal system size, which is a multi-objective problem including the minimization of annualized cost of system (CACS) and deficiency of power supply probability (DPSP). MATLAB software is utilized to program and simulate the hybrid energy system. Optimization results confirm that IMOGWO is feasible to optimally size the system, and the energy management strategy effectively matches the requirements of system operation. Furthermore, comparison of hybrid systems with and without tidal current turbines is undertaken to confirm that the utilization of tidal current turbines can contribute to enhancing system reliability and reducing system investment, especially in areas with abundant tidal energy sources.