The invention concerns a catalyst comprising a porous support, palladium, at least one metal selected from the group constituted by alkalis and alkaline-earths, in which: the specific surface area of the porous support is in the range 50 to 210 m2/g; the palladium content in the catalyst is in the range 0.05% to 2% by weight; at least 80% by weight of the palladium is distributed in a crust at the periphery of the support, the thickness of said crust being in the range 20 to 200 μm; the metallic dispersion D is in the range 25% to 70%; the density of the palladium particles in the crust is in the range 1500 to 4100 particles of palladium per μm2; and said alkali and/or alkaline-earth metal is distributed homogeneously across the support. The invention also concerns the preparation of the catalyst and its use in selective hydrogenation.