A production method of a hydrogenated polymer by hydrogenating aromatic rings of an aromatic vinyl compound-(meth)acrylate copolymer, in which (1) a solvent solution of the copolymer is added to a reactor, which has a solvent and a supported palladium catalyst charged therein, under a hydrogen atmosphere at a rate of from 0.01 to 15 g/hour in terms of the copolymer per unit mass (g) of the supported palladium catalyst, thereby performing hydrogenation reaction, and then such an operation is performed repeatedly that (2) 30 to 90% by mass of the resulting reaction mixed solution is taken out from the reactor, a hydrogenated polymer is obtained from the reaction mixed solution which is taken out from the reactor, and a fresh solvent solution of the copolymer is added to the reactor, in which the residual reaction mixed solution is left, at a rate of from 0.01 to 15 g/hour in terms of the copolymer per unit mass (g) of the supported palladium catalyst, or the total of the resulting reaction mixed solution is taken out from the reactor, a hydrogenated polymer is obtained from 30 to 90% by mass of the reaction mixed solution which is taken out from the reactor, and a fresh solvent solution of the copolymer is added to the reactor, to which the residual reaction mixed solution is returned, at a rate of from 0.01 to 15 g/hour in terms of the copolymer per unit mass (g) of the supported palladium catalyst, thereby performing hydrogenation reaction.