The present invention relates to a method for the selective hydrogenation of an unsaturated compound, particularly a method in an unsaturated compound or a mixture containing unsaturated compounds for increase of the light sulphides weight, hydrogenation of a polyunsaturated compound and isomerization of a monounsaturated compound. The method uses a supported catalyst. The supported catalyst contains at least one Group VIB non-noble metal oxide and at least one Group VIII non-noble metal oxide deposited on a carrier; and the catalyst has an optimized acid distribution on the surface of the catalyst, and more preferably has an optimized Group VIII/VIB metal ratio and a Group VIII non-noble metal density per unit of catalyst surface area.