A supported hydrogenation catalyst composition is disclosed which comprises a palladium component, at least one alkali metal iodide such as, for example, potassium iodide, and an inorganic support material such as alumina. The palladium component is concentrated in an area within about 150 microns of the exterior surface of the composition. Also disclosed is a selective hydrogenation process in which diolefins and/or alkynes are hydrogenated with hydrogen to corresponding monoolefins.