Provided are a selective hydrogenation catalyst exhibiting a superior reactivity and selectivity against an oxygen-containing polar functional group(s) in a compound having a hydrogenation reaction site(s) such as a carbon-carbon double bond and an oxygen-containing polar functional group(s) such as an epoxy bond; a method for producing such selective hydrogenation catalyst; and a method for selectively hydrogenating such compound using this type of selective hydrogenation catalyst. In a method for hydrogenating a compound having a hydrogenation reaction site(s) and an oxygen-containing polar functional groups(s), this compound is brought into contact with a hydrogen gas in a liquid phase under the presence of a selective hydrogenation catalyst with a silver component-cerium oxide complex being supported on a metal oxide support, the silver component-cerium oxide complex including silver component particles and a cerium oxide supported on the surfaces of such silver component particles. Thus, the oxygen atoms in the oxygen-containing polar functional group(s) can be selectively hydrogenated.