Catalysts for copolymerization of olefins and styrenes, comprising (A) a transition metal compound, (B) an oxygen-containing compound and/or a compound capable of reacting with a transition metal compound to form an ionic complex, (C) a specific compound such as a reaction product of triphenylmethyl alcohol and triisobutylaluminium, and optionally (D) an alkylating agent, and methods for producing olefin-styrene copolymers in the presence of such catalysts, which catalysts have the advantages of enhancing the copolymerization activity and reducing the amount of the promoter such as oxygen-containing compounds, etc, and using them, olefin-styrene copolymers can be produced efficiently and inexpensively.