How to improve the performance of piezoelectric vibration energy harvesting (PVEH) with nonlinearities is a key problem in engineering applications. A mathematic model of nonlinear PVEHs was built in this research. A fast numerical method based on the principle of the definite integral was proposed to solve the nonlinear model. Then the effects of these nonlinear parameters on the performance of nonlinear PVEHs were simulated. The results demonstrate that both reducing nonlinear damping and increasing nonlinear piezoelectric coupling coefficients will improve the performance, and reducing nonlinear stiffness will increase the output of low frequency vibration energy harvesting, and decrease its resonant bandwidth. 