Solar cooling is one of the most promising solutions to the worsening energy and climate issues. A solar-driven liquid desiccant evaporative cooling air-conditioning system with solution storage tanks was proposed. The daily performance of the proposed system under the variable solution recirculation ratio (Rs) adjusting method in a typical hot-humid summer day of Nanjing was investigated using a quasi-dynamic mathematical model. The solution storage effect and the coupled characteristics of the solar collecting subsystem and the liquid desiccant cycle were taken into account. The effects of water tank volume (Vwt), the initial solution mass in the solution storage tank (Ms,storage,tank) and the area of solar collector (Asc) on the overall system performance were also evaluated. The results show that with the help of the stored solution, the proposed system can effectively handle the space cooling load during the whole period of operation. The average values of thermal coefficient of performance (TCOP) and solar coefficient of performance (SCOP) are 0.66 and 0.31, respectively. The variable Rs adjusting method can guarantee the required solution concentration and adapt well to the varying solar radiation. When Asc is limited, a smaller Vwt and a larger Ms,storage,tank are recommended to achieve a higher SCOP when covering the required space cooling load.