The technology of selected harmonic elimination pulse width modulation (SHEPWM) can be used to eliminate the selected low-order harmonics and satisfy the demand of desired fundamental voltage by calculating the optimal switching angles, this method has a series advantages such as low switching frequency and high-quality waveforms, etc. In order to improve the reliability and rapidity of calculating for the SHEPWM non-linear equations, this paper presents the stochastic Newton method (SNM) which is composed of the particle swarm optimization (PSO) and the Newton method, the reliability and rapidity of the SNM is verified by a program for SHEPWM non-linear equations. In the end, the simulation experimental systems of seven-level single-phase cascade inverter and eleven-level three-phase D connected cascaded inverter are designed and tested that the selected low-order harmonics are eliminated by the switching angles calculated by the SNM and the fundamental voltage is produced. This work is supported by National Natural Science Foundation of China (No. 51307021) and Natural Science Foundation of Jilin province (No. 20140101076JC).