Pneumatic systems are widely used in industrial manufacturing sectors. However, the energy efficiency of pneumatic systems is generally much lower than their hydraulic and electric counterparts. It is necessary to explore more elaborate theories and methods for achieving better energy performance in pneumatic systems. In this study, for investigating the interaction effects between pneumatic components and the accessible improvement potential of energy efficiency in a pre-existing pneumatic system, the advanced exergy analysis is conducted with a better understanding of exergy destruction. The conventional exergy analysis is also carried out for comparison. The results show that an exergy efficiency of 17.3% could be achieved under the real condition in the case of the investigated pneumatic system. However, under unavoidable conditions, the theoretical maximum exergy efficiency could reach 70.5%. This means there is a significant potential for improving the energy performance of the investigated system. Furthermore, both conventional and advanced exergy analyses indicate that the pneumatic cylinder has the greatest potential for improvement. The advanced exergy analysis reveals the complex and variable interactions between pneumatic components. It highlights that the exergy destruction of some components is caused by other components in the system, and thus, improving energy efficiency at the system level rather than at the component level is of great significance. Besides, a priority order of all pneumatic components is determined, thereby guiding the improvement of the energy efficiency of the pneumatic system.