In this article, a novel multi-stage compression and heat recovery on an adiabatic compressed air energy storage (A-CAES) system is proposed. In the current work, an in-house code named CAESSC 1.0 is successfully developed which can be helpful to evaluate the performance of the proposed A-CAES system and other power generation systems. In order to obtain the optimum performance, thermodynamic analysis of a multi-stage compression A-CAES system is investigated in a systematic manner. The effect of several control parameters, such as gas storage methods, storage pressures, interstage heat transfer methods, and stage numbers of the compressor as well as the turbine on the overall performance of the system is discussed in detail. Results indicate that using constant pressure gas storage method could significantly improve both the energy storage efficiency and the energy storage density of the system. An optimised algorithm of the heat exchanger in CAES system is proposed to remarkably improve the simulation performance. The highest efficiency can exceed 70% when using compressed air with adiabatic method. Two different gas storage methods, i.e. constant volume and constant pressure, have been discussed. It indicates that the efficiency of the system under constant pressure storage is about 4% higher than that under constant volume storage.