The invention relates to an island energy supply system with cold energy. The island energy supply system comprises an LNG power generation system unit, a renewable energy power generation and energy storage unit and a low-temperature multi-effect distillation seawater desalination system. The island energy supply system is a combination island energy supply system formed by power generation and energy storage systems in a combination mode based on an LNG power generator and unstable renewable energy such as wind energy, solar energy and wave energy. System waste heat is used as a heat source for a seawater desalination unit. During an energy storage process, stored LNG is converted into high-pressure natural gas (NG) by cold accumulation gasifying, the NG enters an NG storage tank and a pipe network system for storage and standby application, then air is subjected to compression, indirect cooling and cold accumulation, cold energy is recycled, and after throttling, liquidation storage is carried out. During a power using process, after high-pressure NG absorbs heat and is heated, the high-pressure NG enters a turbine expansion machine for working, then the NG enters a small gas turbine combustion chamber and burns with compressed air to drive a gas turbine to work, and liquid air is subjected to cold accumulation and gradual heat absorption temperature raising and then enters the turbine expansion machine for working. According to the energy supply system, on-island electricity energy and fresh water can be supplied at the same time, unstable renewable resources are converted into stable controllable generated power to be output, system efficiency is improved, power using cost is lowered, and compared with traditional island energy supply system, the island energy supply system has the great advantages.