This paper investigates resonance vibration suppression under persistent excitation near the first structural resonant frequency of a clamped-clamped (doubly-clamped) piezoelectric flexible beam. In this study, an acceleration sensor is used to measure the resonant vibration. Firstly, the finite element method (FEM) is utilized to derive the dynamics model of the system, and modal analysis is carried out. Secondly, an acceleration feedback-based proportional-integral control algorithm and variable structure control algorithms are designed, and a numerical simulation is performed. Finally, a doubly-clamped piezoelectric flexible beam experimental setup is constructed. Experiments are conducted on resonant vibration suppression using the designed control algorithms. The numerical simulation and experimental results demonstrate that the resonant vibration can be suppressed by using the designed control methods, and the improved variable structure control method shows better control performance in suppressing the resonant vibration.