A tri-stable piezoelectric vibration energy harvester with asymmetric and time-varying potential wells is proposed to enhance the energy harvesting performances. It is composed of a piezoelectric cantilever beam with a tip magnet and a pair of external magnets which is fixed to a spring. The spring is fixed at the base and can be compressed and stretched when it is repulsed and attracted by the magnetic force. Based on the magnetic charge method and Lagrange function， the nonlinear magnetic model and distributed parameter dynamic model of piezoelectric vibration energy harvesting system are established. The effects of the distance between magnets， acceleration and spring stiffness on the potential energy and dynamic response characteristics of the system are sim ulated and analyzed. The results show that the spring stiffness makes the depth of the asymmetric potential well shallower， making it easier for the collector to enter the large vibration state. With the increase of the stiffness， the output performance of the collector first increases and then decreases. Under low excitation amplitude， the asymmetric and variable potential well energy collector has wider frequency band width and higher acquisition efficiency than the traditional symmetric potential well collector.