A 11-Level Inverter was designed and implemented with suitable SHE-PWM technique. The problem of eliminating the harmonics is redrafted as an optimization problem and it is solved by using Adaptive Neuro – Fuzzy Inference System (ANFIS). Finding the location of the switching instants in the case of SHEPWM involves the solution of a set of nonlinear algebraic transcendental equations. The problem is redrafted as an optimization problem, and it is solved by using GHNN. Though, in principle, the n number of harmonics can be eliminated using the presented methodology, this paper tries for the case of the elimination of the 5th-, 7th-, 11th-, and 13th-order harmonics while retaining the desired fundamen-tal. An energy function is formulated for this problem and the set of ordinary differential equations (ODEs) describing the behavior of GHNN is obtained. The suitable switching instants for eliminating the harmonics is obtained by solving the non-linear algebraic transcendental equations. An effectiveness of the proposed method is validated using MATLAB simulation.