The potential for an autonomous wave-powered desalination system is considered and it is identified that the most promising configuration is a reverse osmosis (RO) plant utilising a pressure exchanger-intensifier for energy recovery. A numerical model of the RO plant with a pressure exchanger-intensifier is developed that shows that a specific energy consumption of less than 2.0 kW h/m3 over a wide range of sea-water feed conditions, making it particularly suitable for use with a variable power source such as wave energy. A numerical model of the combined wave-power and desalination plant is also developed that shows that it is possible to supply the desalination plant with sea-water directly pressurised by the wave energy converter, eliminating the cost and energy losses associated with converting the energy into electricity and back to pressurised water. For a typical sea-state the specific hydraulic energy consumption of the desalination plant is estimated to be 1.85 kW h/m3 whilst maintaining a recovery-ratio of less than 25 to 35% to avoid the need for chemical pre-treatment to eliminate scaling problems. It is suggested that the economic potential for wave-powered desalination depends on these energy and cost savings more than compensating for the reduction in membrane life that occurs with variable feed conditions.