The dynamic behavior of a piezoelectric cantilever energy harvesting system with bi-stable state under elastic support is studied to reveal its complex phenomena. Based on the magnetic force model which can induce bi-stable phenomena, the mathematical model of the system with two degree of freedom under harmonic base motion is firstly established by using Newton's second law and Kirchhoff′s law. By the Routh-Hurwitz criterion, the static bifurcation of equilibrium points, is secondly analyzed for the dimensionless governing equations. At last, the amplitude variations of the displacement of piezoelectric cantilever beam and the variations of the output voltage with the system parameters and excitation parameters and their bifurcation diagrams are obtained by Matlab numerical simulations. The results show that the amplitude-frequency curves of the system are in hard characteristic, while the amplitude variations of the displacement of piezoelectric cantilever beam with mass ratio and stiffness ratio are in soft characteristic. That is, within some parameters intervals, the harmonic response of the system has bifurcation and leads to chaotic motion. The motion of the system can take place near the zero or non-zero equilibrium point, even jump with large amplitude between the two non-zero equilibrium points. For the same parameters, bi-stable systems have richer forms of motion compared to mono-stable ones, and significantly increase voltage output and response frequency band of the system. The research result may provide theoretical reference for how to optimize vibration energy collector in practice.