Providing clean water to small communities using renewable energy (RE) has long posed as a humanitarian challenge. Reverse osmosis (RO) desalination has been proven as a mature technology for supplying fresh water for different domestic, industrial, and agricultural usages. On the other hand, RE is the targeted future alternative that can drive RO desalination process in many parts of the world. A lot of work has been done on operating desalination processes using either wind or solar energy individually or both energy sources alongside one another. In this paper, a numerical model which would allow finding the optimal design of a hybrid solar-wind power that would drive a small-sized RO desalination plant is presented. The optimized design variables are the number of solar Photovoltaics modules, the number of wind turbines, height of the wind tower, radius of the rotor blade, and the desalination plant capacity. The objective is to obtain a design which would allow us to produce a given amount of fresh water, at minimal cost. As the RO specific energy consumption varies with feed water properties (mainly salinity and turbidity), three values are considered for the present study: 2.5, 5.0, and 7.5 kW/m3. The study shows that the hybrid power plant exploits the complementary nature of the energy sources to achieve water demand. The optimal design values of the hybrid RE system varies with the water demand and for the study's values of specific energy consumption, the specific water cost is found to be 0.498, 0.851, and 1.211 $/m3 respectively.