In order to improve the output performances of the bi-stable piezoelectric vibration energy harvester（BPEH），a multi stable piezoelectric vibration energy harvester formed by the magneto mechanical piezoelectric coupling effect is proposed. By introducing a pair of external magnets into the BPEH，a quad-stable piezoelectric vibration energy harvester（QPEH）is developed. The nonlinear magnetic force and potential energy of the energy harvester is firstly derived based on the magnetic dipole theory，and then the nonlinear dynamic model of the proposed harvester is derived based on the Hamilton principle and the Raleigh-Ritz method. Some simulations are performed to reveal the effect mechanisms of the system parameters on the nonlinear magnetic force and the dynamic characteristics of the energy harvester. A prototype of the QPEH is manufactured and the experimental system is setup. The experimental results are well agreeable with the simulation results，which testified the proposed dynamic model is correct. The results show that the QPEH oscillating into a quad-stable motion generates wider bandwidth and higher output performance than those of it oscillating into a bi-stable motion.