This article presents the application of the harmony search (HS) optimization algorithm for selective harmonic elimination PWM (SHEPWM) in a new topology of multilevel inverters with reduced number of electronic switching elements. The main objective of the harmonic elimination strategy is eliminating undesired low-rank harmonics in order to improve the quality of the output waveform. The harmonic elimination strategy is achieved by solving a system of nonlinear equations. In this paper harmony search optimization is applied using artificial neural networks (ANNs) on a new 21-level inverter topology. The algorithm is based on a music improvisation process. MATLAB programming software is used to develop a harmony search optimization program for harmonic elimination. A small-scale laboratory of the proposed 21-level inverter is built to validate the simulation results and to prove the efficiency of the proposed control scheme.