The aim of this study is to investigate theoretically the effect of different system operating conditions, types of air heater, and some different design parameters and a weather condition on a solar water desalination system performance under the climatological conditions of Ankara (40 degrees N,33 degrees E), Turkey. For this purpose, a computer simulation program based on the mathematical model is developed by means of MATLAB software. In this simulation program, the fourth order Runge-Kutta method is used to solve the energy balance equations numerically. The desalination unit is configured by a double-pass flat plate solar air heater with two glass covers, humidifying tower, storage tank and dehumidifying exchanger. The system used in this work is based on the idea of closed water and open air cycles. Air is heated by using a double-pass solar air heater whereas water is not heated. The system productivity is increased up to 9% by using a double-pass solar air heater compared to a single-pass solar air heater and decreased about 30% without double-pass solar air heater under the same operating conditions. Significant development on the productivity of the system is achieved by increasing the humidifier inlet water and air mass flow rates. At a constant water mass flow rate, however, the productivity of the unit increases with the increasing of air mass flow rate to an optimum value and decreases after that value. In addition, theoretical results indicate that there is a significant improvement on the system performance as the inital water temperature and water mass in the storage tank is increased. Moreover, increasing the cooling water mass flow rate and decreasing its temperature lead to appreciable improvement on the unit productivity. It is also found that, the system performance is strongly affected by the double-pass solar air heater area and slightly influenced by the bottom heat loss coefficient of the solar air heater and storage tank (especially, when its temperature is lower than the ambient air temperature). Finally, the productivity of the unit that consists of a double-pass solar air heater with two glass covers is not influenced by the wind speed variations as much as double-pass solar air heater with one glass cover.