Abstract: In order to improve the dynamic output performance and environmental adaptability of the tri-stable piezoelectric energy harvester （TPEH）， a new flexible tri-stable piezoelectric energy harvester （FTPEH） with double flexible auxiliary beams for real-time adjusting the potential well depth and barrier height is proposed. Based on the traditional magnetic coupling tri-stable piezoelectric energy harvester， two auxiliary flexible beams with the same structure and size are introduced， and the two external magnets are fixed at the tip ends of the two auxiliary flexible beams. When the harvester is excited by the external excitation， the two auxiliary beams oscillate with slight amplitude in the horizontal direction， thus the horizontal distance between the external magnets and the tip magnet of the piezoelectric cantilever beam can be adjusted in real-time， so as to tune the potential energy well depth and barrier height， resulting in improving the dynamic output performance and environmental adaptability. The electromechanical coupling dynamic model describing the dynamic responses of the new tri-stable piezoelectric energy harvester is established based on Euler Bernoulli theory and Hamilton principle， and the influences of system parameters on the nonlinear magnetic force and dynamic performance are simulated and analyzed. Compared to the traditional tri-stable harvester， the new tri-stable harvester has a wider bandwidth of inter-well motion and lower excitation for jumping from intra-well motion to inter-well motion.