The Multilevel Inverter (MLI) uses Selective Harmonic Elimination (SHE) of the Pulse Width Modulation (PWM) approach to tackle the fundamental harmonics with the elimination of selected lower harmonics. The optimal switching angle for this PWM method is calculated by solving a set of nonlinear equations. The PWM signal is generated using these angles in a real time system. Modified Quantum Particle Swarm Optimization (MQPSO) is implemented in this paper to provide the optimal angle for generating the PWM signal. In this study, 5 optimal switching angles for a single-phase 11-level MLI have been calculated. It is observed that MQPSO produces optimal switching for modulation indices between 0.4 and 0.7. To obtain a quarter-wave symmetry bipolar waveform output voltage, the MQPSO based SHE-PWM has been developed and implemented by using MATLAB Simulink. The output voltage and harmonic spectrum of the proposed system are also obtained using MATLAB. Furthermore, the results are also compared with another modulation technique to validate the superiority of MQPSO based SHE-PWM. The Total Harmonic Distance (THD) has been reduced by 3.62% compared to Nearest Level Control (NLC), which has verified that the proposed method has successfully eliminated the low-order harmonics.