A solar heated membrane distillation desalination system is constructed of solar collectors and membrane distillation devices for increasing pure water productivity. This technically and economically feasible system is designed to use indirect solar heat to drive membrane distillation processes to overcome the unstable supply of solar radiation from sunrise to sunset. The solar heated membrane distillation desalination system in the present study consisted of hot water storage devices, heat exchangers, air gap membrane distillation units, and solar collectors. Aspen Custom Molder (ACM) software was used to model and simulate each unit and establish the cost function of a desalination plant. From Design degree of freedom (DOF) analysis, ten design parameters were investigated to obtain the minimum total annual cost (TAC) with fixed pure water production rate. For a given solar energy density profile of typical summer weather, the minimal TAC per 1 m3 pure water production can be found at 500 W/m2 by varying the solar energy intensity. Therefore, we proposed two modes for controlling the optimal design condition of the desalination plant; day and night. In order to widen the operability range of the plant, the sensitivity analysis was used to retrofit the original design point to lower the effluent temperature from the solar collector by increasing the hot water recycled stream. The simulation results show that the pure water production can be maintained at a very stable level whether in sunny or cloudy weather.