A process for producing a hydrogenated polymer, which includes a step of hydrogenating aromatic rings of an aromatic vinyl compound--(meth)acrylate copolymer. In the process, the copolymer having a ratio, A/B, of from 0.25 to 4.0 (A is a molar number of constitutional units derived from the (meth)acrylate monomer, and B is a molar number of constitutional units derived from the aromatic vinyl monomer) is hydrogenated in a solvent in the presence of a catalyst which is composed of zirconium oxide supporting palladium. By the process, a highly transparent, hydrogenated polymer is stably and rapidly produced for a long period of time or repeatedly.