A model predictive controller for a wave-powered desalination unit is presented. The desalination unit is composed of a reverse osmosis membrane, and the water is pumped at high pressure through the membrane by a wave energy converter. The wave energy converter is a heaving buoy type connected to an hydraulic circuit that converts the oscillating motion of the buoy into a rectified sea-water flow at high pressure. The controller acts on a throttle valve to regulate the pressure in the reverse osmosis unit in order to avoid damage to the membrane caused by excessive pressure and to improve both its longevity and the overall efficiency of the device. The control is constrained due to the rate and position limits of the throttle valve and the recovery ratio, which is the ratio between the total amount of pumped sea-water and the potable water. The system is also switched and non-stationary because of the check valves used for the rectification of the sea-water flow and the variation of the excitation force dynamic over time, respectively. Results are presented using a nonlinear simulation model for the plant, using both monochromatic and real sea states.