The catalyst includes alumina, RE metal oxide, composite Al-La oxide, and active metal Pt, Pd and Rh. It features that the mixed oxide grain with aluina, cerium oxide and Al-La oxide carries at least one of Pt and Pd as well as Rh. The mixed oxide grain is prepared through dissolving salt of Al, Ce and La in water, adding NH3OH to produce precipitate, and heating to decompose the precipitate. The catalyst preparing process includes carrying mixed oxide grains onto the carrier, carrying least one of Pt and Pd onto the mixed oxide grains, and carrying Rh finally. The catalyst is especially suitable for purifying automobile tail gas of gasoline engine near the theoretical air/fuel ratio, and has the features of lasting use, less noble metal consumption, high purifying efficiency and powerful sulfur poison resistance.