A systematic modeling method is proposed to predict the overall efficiency and power requirement of a multistage air-compression system consisting of a multistage compressor, a multistage expander, and an electric motor/generator. First, under a lack of measurements at the interstages of the multistage compression system, a calculation method of the overall efficiency is developed based on thermodynamic compression and expansion equations. Then, the prediction structure of the overall efficiency and actual power consumption/generation rate of the compression system is presented, where either partial least-squares models or artificial neural network models can be employed to predict unknown state variables and the overall efficiency, which are, in turn, used to predict the actual power consumption/generation rate based on compression and expansion equations. Finally, to verify the proposed modeling method, it is applied to two industrial compression systems of a terephthalic acid manufacturing process, and the comparisons with measurements show excellent prediction performances both in the overall efficiency and in the actual power consumption rate. The proposed modeling method can be applied to find better operating conditions of compression systems in various chemical processes.