In this paper, the dynamical behaviors of a tri-stable piezoelectric energy harvester under the narrow-band random excitation is studied. Firstly, the dynamical equation of a tri-stable nonlinear cantilever piezoelectric energy harvesting system is established. The analytical expressions of the dynamical response of the system together with the first and second steady moments are obtained by using the multiple scales method. Secondly, the effects of the distance between the tip magnet and the external magnets, the noise intensity and the excitation amplitude on the system response and harvesting performance are discussed. The obtained results show that as the noise intensity increases, the piezoelectric vibration energy harvester will experience mono-stable, bi-stable and tri-stable motion. Changing the horizontal and vertical spacing of the magnets makes the piezoelectric energy harvester perform tri-stable motion, and the displacement and acquisition voltage are significantly improved compared to the bi-stable case. Finally, the collection performance of the piezoelectric energy harvester in different configurations is compared through experiments.The results show the superiority of the tri-stable piezoelectric energy harvester, which provide the theoretical support for the design of the vibration energy harvester under the narrow-band random excitation.