Disclosed are a catalyst, its preparation and use in selective hydrogenation, which catalyst has a porous support grain on which are deposited palladium and silver, and at least one alkali and/or alkaline earth metal; the porous support contains a refractory silica, alumina and/or silica-alumina oxide, where at least 80 wt. % of the palladium is distributed in a crust at the periphery of the support, and at least 80 wt. % of the silver is distributed in a crust at the periphery of the support, the local content of palladium at each point along the diameter of the grain follows the same course as the local content of silver.