Inverters are such electronic devices that are extensively used to convert DC power to AC power in wide-range domestic and industrial applications. DC power is usually supplied from either national grid through the rectifiers or batteries for high and low energy demands, respectively. When they are employed to feed electrical devices the efficiency of these devices tends to decrease due to harmonic occurrence in them. One solution to this problem is the selective harmonic elimination which is required to solve multiple non-linear equations simultaneously. These equations are mainly function of the switching angles and are obtained from a type of inverter output voltage such as being unipolar, bipolar, etc. To eliminate one or more harmonics in these output voltages becomes a typical multivariate root-finding problem and its solution requires root-finding methods such as the Newton–Raphson method, the Broyden method etc. These methods can only produce a meaningful solution if initial values are properly guessed, but it is highly difficult task due to having no direct formula. In this paper, the hybrid genetic algorithm method based on the refinement of the genetic algorithms results through the Newton–Raphson method was used to simultaneously solve the non-linear equations. The results have shown a considerable effect on decrease in the total harmonic distortion, thereby increasing the efficiency of devices compared to conventional methods under the same conditions.