The compressors in the air conditioner have the role of the pressurization and circulation of the refrigerant. The hermetic reciprocating compressors driven by rotary motor have been used for the air conditioner. The linear compressor has very simple structure and enhancement in the efficiency in comparison to that of conventional reciprocating compressor. The linear compressors are widely used for the small cryogenic refrigerator (below 1 kW), such as the Stirling refrigerator and pulse tube refrigerator. In the cryogenic application, the pressure ratio of the linear compressor is below 1.5, but the linear compressor for the air conditioner should overcome the high pressure ratio and the large pressure difference between the each sides of the piston. The resonance characteristics of the linear compressor has the significant impacts on the power consumption. To minimize the power consumption, the linear compressor should be operated at the resonance point. In the resonance characteristics, the role of the mechanical and gas spring should be considered. In present study, the cycle of the analysis of the vapor compression refrigeration cycle with the different refrigerants (R134a, R4l0a, R600a) and the designs of the linear compressor are performed. The effects of the stiffness of the mechanical spring on the electromagnetic forces would be discussed. Finally, the results show the design specification of the linear compressor for the air conditioner.