Fresh water is rapidly becoming a scarce resource in many countries around the world. Modern desalination technologies, applied to seawater and brackish water, offer effective alternatives in a variety of circumstances. Out of the several desalination processes considered, reverse osmosis is one of the major processes used in desalination. Reverse osmosis is in general the most economical process for desalination of brackish water and seawater. As widely accepted technology, reverse osmosis became more and more competitive and is superior to the traditional thermal process when a comparison is made of capital investment and energy consumption. The present study pertains to modeling numerically of a seawater desalination system. The proposed method considers solving the momentum, energy and mass transfer conservation equations for a smallscale reverse osmosis system. The solution of the conservation equations was obtained using the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) pressure-correction scheme and the high order discretization scheme QUICK (Quadratic Upwind Interpolation Convective Kinematics) is employed for the discretization of convection terms in the frame of staggered grid. The model was verified using the experimental data from the literature. Parameter sensitivity was carried out to select the proper time and spatial step sizes. The calculations were run for a very long time enabling a prediction of operational performance at high overall system recoveries. Effects of the feed temperature variations on the operating parameters are also considered in this study.