The invention discloses a selective hydrogenation catalyst for producing biodiesel and a preparation method and application of the selective hydrogenation catalyst. The selective hydrogenation catalyst comprises a carrier and a main metal active ingredient loaded on the carrier, the main metal active ingredient accounts for 5-30% of the catalyst in weight and is one of or a combination of oxides containing Co, Mo, Ni and W, and the carrier is composed of, by weight, 1-8% of a molecular sieved, 25-65% of amorphous sial, 30-65% of alumina and 2-10% of a graphene auxiliary. The preparation method includes: disposing the carrier in a metal salt solution containing Co, Mo, Ni or/and W for soaking for 4-20 h to obtain a soaked carrier; freeze-drying and then calcining the soaked carrier to obtain the selective hydrogenation catalyst. With same carrying capacity of the carrier, active surface area represented by the carrier is large, the selective hydrogenation catalyst has more active sites, reaction temperature is lowered, and hydrogenation performance is improved.