A catalyst for the selective hydrogenation of alkynes and dienes in C2-C5.sup.+-olefin mixtures is described.These catalysts contain (a) a metal of the tenth group of the Periodic Table, (b) a metal of the eleventh group of the Periodic Table and (c) if required, a compound of a metal of the first or second group of the Periodic Table, these metals being applied to a support which is selected from the group consisting of silica, titanium dioxide, zirconium oxides, spinels, zinc aluminates, zinc titanates or mixtures of these substances, and the metal of the eleventh group being distributed homogeneously over the cross section of the catalyst particle and the metal of the tenth group being present in the edge layer close to the surface of the catalyst particle. Such a catalyst is prepared by applying the metal of the eleventh group, preferably during the preparation of the support itself, by impregnation with a solution of a suitable metal salt.