Compressed-air energy storage in aquifers (CAESA) has garnered considerable attention as a crucial large-scale energy storage technology in recent years, under the context of global energy transition and the “dual-carbon” goals. This study proposes an underground CAESA system and presents a transient simulation of the cyclic injection and extraction of compressed air within an anticlinal aquifer structure, conducted using CMG software. Data interaction and calculations were performed using a Matlab/Simulink platform. Under the design operating conditions, the evolution of bottom-hole pressure throughout the cyclic injection and extraction processes was simulated, effectively achieving coupling between dynamic operation conditions of the surface thermal system and the real-time evolution of underground aquifer injection and production. The simulation analyzed the response characteristics of key state parameters, adiabatic efficiency, and input power at each stage of the compressors and turbines during compression and expansion. The results indicate that, under the design conditions, the outlet density, temperature, pressure, power consumption, and adiabatic efficiency of each compressor stage during the compression process, as well as the outlet temperature and mass flow rate of the high-temperature heat transfer oil, exhibit an upward trend. After three-stage expansion, the air pressure decreases from 2.087 MPa to atmospheric pressure and the air density drops from 19.09 to 0.904 kg/m3. Owing to the progressively decreasing expansion ratio, the work output of the turbine stages diminishes, resulting in sequentially increasing outlet temperatures. When the adiabatic efficiency remains constant at 0.8, the power consumption follows the order WHT>WMT>WLT; the mass flow rate and temperature of the heat transfer oil increase first and then decrease as heat exchange occurs during the expansion process. The above-ground and underground components of the entire system operate smoothly, and the energy storage efficiency under the design conditions reaches 62.77%.