Harmonics can be characterized as components with periodic waveforms having multiples of a fundamental frequency. Harmonics, one of the most critical issues of power quality, have recently come into prominence despite being known in advance. Many scientists and researchers have suggested various methods for decreasing or eliminating these low-order and high-order harmonics since the early time of the ac power systems. Selective Harmonic Elimination Method (SHEM) in the proposed methods is shown superior performance on low-order harmonics in low switching frequencies. Various Meta-Heuristic Algorithms (MHA) are used to solve the equations included in this method and to reduce the computational burden. In this study, Grey Wolf Optimizer (GWO) which is a metaheuristic method added to literature in recent history, is applied to 3-phase Voltage Source Inverter (VSI) system using SHEM for harmonic elimination. GWO technique is analyzed and implemented for calculating the switching angles for Voltage Source Inverter (VSI). Total harmonic distortion (THD) values of GWO and without GWO methods of the inverter system are also compared with Cuckoo Search (CS) and Genetic Algorithm (GA). Our results show that using GWO method eliminates low-order harmonics and reduces THD value of the system according to power quality standards.