The invention discloses a Cu-Zn catalyst, a precursor, a preparation method and an application thereof. The Cu-Zn catalyst takes a mesoporous molecular sieve as a carrier to load active components comprising cuprum and zinc. The preparation method comprises the following steps: the mesoporous molecular sieve is added into a water solution holding cuprum ions and zinc ions for soaking, filtered to obtain solid filter cakes which are mixed with a bonder and a bonding aid for prilling, then dried, roasted and cooled, thus obtaining the precursor of the Cu-Zn catalyst of the invention, or the mesoporous molecular sieve also can be mixed with the bonder and the bonding aid for prilling, added to the water solution holding the cuprum ions and the zinc ions for soaking, then dried, roasted and cooled. The precursor of the Cu-Zn catalyst of the invention is deoxidized in a reduction atmosphere to obtain the Cu-Zn catalyst of the invention. The Cu-Zn catalyst of the invention not only has good catalyzing efficiency, but also has good stability, high catalytic activation and relatively long service life, thus being able to be applied to the reaction of high temperature and high pressure catalytic hydrogenation of fatty acid ester or the preparation of fatty alcohol by hypercritical catalytic hydrogenation.