Islands are the main platforms for exploration and utilization of marine resources. In this paper, an island hybrid renewable energy microgrid devoted to a stand-alone marine application is established. The specific microgrid is composed of wind turbines, tidal current turbines, and battery storage systems considering the climate resources and precious land resources. A multi-objective sizing optimization method is proposed comprehensively considering the economy, reliability and energy utilization indexes. Three optimization objectives are presented: minimizing the Loss of Power Supply Probability, the Cost of Energy and the Dump Energy Probability. An improved multi-objective grey wolf optimizer based on Halton sequence and social motivation strategy (HSMGWO) is proposed to solve the proposed sizing optimization problem. MATLAB software is utilized to program and simulate the optimization problem of the hybrid energy system. Optimization results confirm that the proposed method and improved algorithm are feasible to optimally size the system, and the energy management strategy effectively matches the requirements of system operation. The proposed HSMGWO shows better convergence and coverage than standard multi-objective grey wolf optimizer (MOGWO) and multi-objective particle swarm optimization (MOPSO) in solving multi-objective sizing problems. Furthermore, the annual operation of the system is simulated, the power generation and economic benefits of each component are analyzed, as well as the sensitivity.