This paper proposes an optimized harmonic reduction pulse width modulation (HRPWM) control strategy for three-phase quasi Z-source inverter (qZSI). In traditional sinusoidal or space vector pulse width modulation techniques, the flexibility in adjustment of individual switching angles is not possible and thus, these techniques are not optimum choices for low switching frequency operations of high/medium power qZSI. In the proposed technique, adjustments of switching angles of HRPWM waveform are possible to achieve optimum performance. The optimum performance is targeted as maximization of boosting factor and simultaneous minimization of weighted total harmonic distortion (WTHD) at the output voltage of qZSI. The hybrid particle swarm optimization gravitational search algorithm (PSOGSA) is used for computation of optimum switching angles of suggested HRPWM waveform at various modulation indices. The obtained WTHDs up to 49th order harmonics and boosting factors of optimized HRPWM methodology are compared with that of the maximum boost control (MBC) technique for qZSI to justify superior performances of the suggested method in low switching frequency range. The proposed concept has been verified via simulation study. The experimentation (qZSI controlled by microcontroller) validates the working of optimized HRPWM based qZSI which agrees with software results.