In this paper, the dynamic behavior of a piezoelectric cantilever energy harvesting system with bi-stable state under elastic support is studies.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 using Newton's second law and Kirchhoff's law. By the Routh-Hurwitz criterion, the static bifurcation of equilibrium point is secondly analyzed after reducing the dimensionless governing equation. In addition, the variation of the piezoelectric cantilever beam and the variation of the output voltage with the system parameters and excitation parameters and the bifurcation diagram are obtained by Matlab numerical simulation. The results show that the amplitude-frequency curves of the system are in hard characteristic. However the variation of the amplitude of piezoelectric cantilever beam with mass and stiffness ratio are in soft characteristic. That is, within some parameters, the harmonic response of the system occurs 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. Under the same parameters, the system has a richer form of motion when it is in bi-stable relative mono-stable state, and significantly increases the voltage output and response frequency band of the system.