The rolling piston type rotary compressor has been widely used for refrigeration and air-conditioning systems due to its compactness and high-speed characteristics. However, it is necessary to develop alternative refrigerants that can guarantee environmental protection. In addition, advanced refrigerant compressors must be further developed to overcome the compatibility problems inherent in refrigeration and air-conditioning systems. The refrigerant compressor is the most important mechanical component, which determines the performances of refrigeration and air-conditioning systems. Therefore, we theoretically investigated the lubrication characteristics of the rotary compressor currently used in both refrigeration and air-conditioning systems with an alternative refrigerant. In the theoretical investigation, the Runge-Kutta method is used to analyze the behavior of a rolling piston in the rotary compressor. Subsequently, the Newton-Raphson method is used, which provided good performance in the analysis of the elastohydrodynamic lubrication of the line contacts between a rolling piston and a vane in the rotary compressor. The results demonstrate that the alternative refrigerants influence the friction force and the energy loss between the vane and the rolling piston.