In supersonic flowing plasmas, the auto-resonant behavior of ion acoustic waves driven by stimulated Brillouin backscattering is self-consistently investigated. A nature of absolute instability appears in the evolution of the stimulated Brillouin backscattering. By adopting certain form of incident lights combined by two perpendicular linear polarization lasers or polarization rotation lasers, the absolute instability is suppressed significantly. The suppression of auto-resonant stimulated Brillouin scattering is verified with the fully kinetic Vlasov code.