A catalyst comprises an active phase constituted by palladium, and a porous support comprising at least one refractory oxide selected from the group constituted by silica, alumina and silica-alumina, in which: the palladium content in the catalyst is in the range 0.0025% to 1% by weight with respect to the total weight of catalyst; at least 80% by weight of the palladium is distributed in a crust at the periphery of the porous support, the thickness of said crust being in the range 25 to 500 μm; the specific surface area of the porous support is in the range 1 to 50 m2/g; the metallic dispersion D of the palladium is less than 20%.