The invention discloses a suppression device and method for shaft system torsional vibration of a compressed air energy storage system. The device comprises an additional excitation damping controllerwhich is used for taking a low pressure cylinder rotate speed signal of a combined air turbo expander as a feedback signal; a generator terminal subsynchronous damping controller which is used for generating a compensation current reference value by taking the low pressure cylinder rotate speed signal of the combined air turbo expander as the feedback signal; and a coordinator which is used for controlling the additional excitation damping controller and the generator terminal subsynchronous damping controller to carry out coordinative work, thereby jointly realizing the purpose of suppressing the shaft system torsional vibration of the compressed air energy storage system. According to the device, variable working condition can be realized through adoption of a flexible shaft system of the combined air turbo expander with a plurality of clutches, the purpose of suppressing the shaft system torsional vibration of the compressed air energy storage system can be realized, the shaft system torsional vibration problem possibly occurring in grid-connected operation of the compressed air energy storage system can be effectively solved, and the grid-connected operation security of the compressed air energy storage system can be effectively improved.