A heterogeneous catalyst for selectively hydrogenating a copolymer is provided, which includes a porous support, a metal oxide wrapping a part of the surface of the porous support, and a plurality of palladium particles on the porous support and the metal oxide. A method for selectively hydrogenating a copolymer is also provided, which includes contacting a heterogeneous catalyst to a copolymer to process hydrogenation. The copolymer includes aromatic rings and nonaromatic double bonds, and the nonaromatic double bonds are hydrogenated, and the aromatic rings are substantially not hydrogenated. The catalyst and the method can selectively hydrogenate double bonds of copolymer.