To obtain a catalyst for copolymerizing isobutylene with styrene, capable of producing a relatively low-molecular-weight copolymer in a high yield by a high-temperature cationic polymerization by making the catalyst include a specific dialkylaluminum halide and a cocatalyst.

This catalyst comprises a dialkylaluminum halide of the formula (R1 and R2 are each a 1-10C alkyl or a 7-10C aralkyl; X is a halogen) such as dimethylaluminum chloride, a cocatalyst such as water and more preferably a metal halide such as titanium tetrachloride or tin tetrachloride. Preferably, isobutylene is copolymerized with styrene in the presence of the catalyst at 10-50°C to produce an isobutylene-styrene copolymer useful as a resin chloride for a hot-melt adhesive, a pressure-sensitive adhesive, or the like, a softener for rubber, or the like.