PURPOSE: To prepare the titled copolymer having excellent heat resistance and suitable as an industrial material, building material, and packaging material, in high efficiency, by copolymerizing an aromatic vinyl compound with a maleic acid half ester in the presence of rubber, and cyclizing the half ester by removing alcohol therefrom.

CONSTITUTION: A reaction system is added with an aromatic vinyl compound (e.g. styrene, α-methylstyrene, etc.), a rubber (e.g. polybutadiene) and a maleic acid half ester (e.g. mono-n-butyl maleate), and if necessary, with other vinyl compounds[e.g. (meth)acrylonitrile, (meth)acrylic acid ester, etc.], catalysts (e.g. dicumyl peroxide), polymerization regulators (e.g. mercaptan), and solvents (e.g. toluene), and the monomers are copolymerized preferably at 70W160°C to obtain the objective copolymer. The polymerization is carried out batchwise or continuously by bulk polymerization, solution polymerization, etc.