The present invention provides an industrially advantageous process for producing a hydrogenated polymer comprising subjecting a polymer having an olefinic carbon-carbon double bond and hydroxy group and/or a functional group which is convertible into hydroxy group or convertible into hydroxymethyl group to hydrogenation under the presence of palladium on a basic activated carbon and/or platinum on a basic activated carbon. The process of the present invention can produce a hydrogenated polymer having hydroxy group and/or a functional group which is convertible into hydroxy group or convertible into hydroxymethyl group with high retention of a functional group and can achieve a high hydrogenation ratio together with good hydrogenation rate.