In this paper, modified multilevel inverter, via addition of an auxiliary bidirectional switch, based on Newton Raphson (NR) and Particle Swarm Optimization (PSO) techniques is presented. The NR and PSO techniques were employed for selective harmonics elimination (SHE) solution in a modified Cascaded H Bridge Multilevel inverter (CHB-MLI). The Selective Harmonic Elimination Pulse-Width Modulation (SHE-PWM) is a powerful technique for harmonic minimization in multilevel inverter. The NR and PSO techniques were used to determine the switching angles by solving the nonlinear equations of the output voltage waveform of the modified CHB-MLI in order to control the fundamental component and eliminate some low order harmonics. The proposed NR and PSO techniques are capable to minimize the Total Harmonic Distortion (THD) of the output voltage of the modified inverter within allowable limits. This paper aims to modeling and simulation by MATLAB of the modified topology of the CHB-MLI for a single-phase prototype for 13-levels. The inverter offers less THD and greater efficiency using PSO control algorithm compared with the NR algorithm. The performance of the proposed controllers based on NR and PSO techniques is verified through simulation.