This study analyzed the performance of solar chimney system for natural ventilation in underground space. A mathematical model of the solar chimney was proposed in order to predict its performance under varying parameters and Korea climatic condition. Steady state heat transfer equations were set up using a energy balanced equations and solved using a inverse matrix method. Numerical simulation program to analyze system was developed by using MATLAB. As the results, the ventilation performance of the solar chimney was determined by the temperature difference of air channel and inlet, and the temperature difference was influenced by insolation, stack height and distance of air gab. Also the solar chimney system can provide $262.9m^3/h$ of annual average ventilation rate. Because seasonal differences of ventilation rate was calculated within 25%, the solar chimney system can be used for every season in Korea climatic condition. Through this study, performance of solar chimney system for natural ventilation was verified by numerical method. Consequently, the solar chimney system is proved to be effective device for natural ventilation utilizing at all times, and the additional studies should be made through the experimental method for imagineering and commercialization.