With the rapid development of China's space industry, flexible structures are more and more widely used in spacecraft development, and vibration control has become the main challenge of spacecraft stability. In this paper, the vibration control of spacecraft flexible structure is taken as the research goal, the basic characteristics and piezoelectric equations of piezoelectric materials are systematically introduced, the modeling and active vibration control of piezoelectric flexible structure are studied, and the vibration control of piezoelectric flexible structure is established. In this paper, an experimental platform for active control is built, and vibration measurement and control experiments are carried out on the experimental platform, which verifies the effectiveness of PID control algorithm based on BP neural network for vibration control, provides theoretical data support for active vibration control of engineering piezoelectric structures, and also provides reference for the research of similar systems with engineering practicability in the future.