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This research paper describes Selective Harmonic Eliminating Pulse Width Modulation (SHEPWM) amalgamated Genetic Algorithm (GA) based asymmetrical Multi Level Inverter (MLI)(15 Level) investigated by using Field Programmable Gate Array (FPGA) for single phase inverter. Multilevel inverter (MLI) have been frequently used in industry particularly to get superior quality output voltage in terms of Total Harmonic Distortion (THD). In SHE PWM equations are capable of determining the required band of switching angles to eliminate desired value of harmonics. GA algorithms playing with band of switching angles randomly to find out best solution for the MLI. Linear feedback shift register (LFSR) has been used to find the random selection of particular switching angles from the band of switching angles. Hence, the proposed method does the capable of eliminating a huge number of specific harmonics and the output voltage results in a minimum THD value. The simulation results show that the proposed method successfully attains the global solution faster than other algorithms. The de-tailed spectrum and FPGA results are presented.