The piezoelectric drive flexible micro/nano positioning platform usually presents a low-damping resonance mode, and it is easy to excite mechanical resonance during high-speed motion, which seriously affects the stability of the control system, control bandwidth and trajectory tracking accuracy. In order to eliminate the dependence of the current resonant controller on the platform dynamics modeling accuracy, an adaptive notch filter is designed to realize the online real-time resonance suppression of the piezoelectric micro/nano positioning platform. Firstly, a piezoelectric drive flexible micro/nano positioning platform system is built and its electromechanical coupling dynamic model is established. Secondly, the fast Fourier transform method is used to analyze the closed-loop system error signal online, and the platform frequency characteristic extraction algorithm is designed to realize the online adaptive tuning of notch filter parameters. Finally, the designed adaptive notch filter is used to carry out trajectory tracking experiments on step signal and triangle wave signal. The experimental results show that the adaptive notch filter can achieve online suppression of resonance, which can effectively improve the stability and trajectory tracking accuracy of the platform.