The invention discloses a composite power compressor. The composite power compressor comprises an engine, a generator, a motor and a compressor, wherein the compressor adopts an open-type compressor with an extension driving shaft, the compressor can be driven by the engine and the motor, and power can be generated. The invention further discloses an air conditioning system. The air conditioning system comprises two or more than two compressors, wherein at least one compressor adopts the composite power compressor, and the composite power compressor can be used for generating power so as to drive other compressors. The invention further provides a control method of the air conditioning system. According to the composite power compressor, the air conditioning system and the control method of the air conditioning system, electric power and natural gas can be adopted, complementary advantages of electric power and natural gas are realized, multiple operating modes are provided, and especially, the heat efficiency of gas heating is higher than that of direct boiler combustion for many times in winter, so that gas resources can be greatly reduced.