In the respect of the environmental protection viewpoint, $CO_2$ may be one of the most attractive alternative refrigerants for an automotive air-conditioning system. For the development of control algorithm of a $CO_2$ automotive air-conditioning system, characteristics of a $CO_2$ refrigerant should be considered. The high-side pressure of a $CO_2$ system should be controlled in order to improve the system efficiency. In this study, dynamic physical models of a $CO_2$ system were developed and dynamic behaviors of the system were predicted by using these models. Control algorithms of a $CO_2$ system were also developed and the effectiveness of these algorithm was verified by using dynamic models.