Selective Harmonic Elimination Pulse Width Modulation (SHEPWM) effectively reduces grid-side harmonics in rectifiers through precise control of power device switching timing. Its main challenge lies in solving the associated nonlinear equation system for switching angles. To address this, this paper proposes applying a Predatory Strategy Genetic Algorithm (PSGA) to a three-phase SHEPWM rectifier. This overcomes the dependence on initial values inherent in traditional numerical methods for solving the switching angles. Furthermore, a Quasi-Proportional Resonant (QPR) controller is integrated into the current loop for enhanced attenuation of grid-side harmonics. Finally, simulation software is adopted to assess the designed control scheme, with comparative analysis against Space Vector PWM (SVPWM) to verify its effectiveness.