Disclosed is a method for selectively hydrogenating a copolymer, including contacting a heterogeneous catalyst with a copolymer to process hydrogenation The copolymer includes aromatic rings and double bonds, and the double bonds are hydrogenated, and the aromatic rings are substantially not hydrogenated. The heterogeneous catalyst includes a metal catalyst such as platinum, palladium, platinum -iridium alloy, or platinum-rhenium alloy formed on a porous support. The hydrogenation is processed at a temperature of 40° C. to 150° C. under a hydrogen pressure of 10 kg/cm2 to 50 kg/cm2.