The rapid development of new energy sources, such as offshore wind power and photovoltaic power, has provided a new solution to the problem of power supply for islands far from the mainland. Wave energy is a kind of renewable energy originated from the ocean, but the existing island power supply programs seldom consider this favorable natural condition. In addition, seawater variable‐speed pumped storage is a new idea to consume offshore wind power and improve the reliability of coastal and island power systems. In view of the stochastic and intermittent nature of new energy sources, this paper adopts seawater variable‐speed pumped storage power plants as energy storage equipment, and put forward an island power supply scheme with wind power, photovoltaic power generation, wave power generation, pumped storage power plants and diesel generator sets as a multifunctional complementary isolated grid. Firstly, wave energy generators, wind farms, photovoltaic farms, pumped storage power stations and diesel generator sets are modeled separately. Then, considering their respective operating conditions, constraints and load requirements, the optimal scheduling of island microgrids with multi‐energy complementarity is constructed. Finally, based on the improved particle swarm optimization algorithm, the model is solved. According to the wind power photovoltaic and wave power output curves of several typical scenarios in an island far away from the mainland, the cost and benefit of different schemes are compared to verify the effectiveness of the optimal scheduling in this paper. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.