To provide a catalyst for copolymerization of styrene and an olefin easily synthesizable, having high polymerization activity in a wide temperature range, capable of controlling a styrene content, capable of performing random copolymerization in which styrene content exceeds 50 mol%, and hardly affected by impurities in the polymerization system.

The catalyst for copolymerization of styrene and an olefin comprising a titanium complex component (A) expressed by CpTiLmX3-m and an activating agent (B) consisting of an alkylaluminumoxy compound or a boron compound (in the formula, Cp is a group having a cyclopentadiene-type anionic skeleton; L is a chelating anionic ligand whose coordinated atom is oxygen; X is H, an alkyl, an alkoxy or the like; and m is an integer of 1-3). A method for producing a styrene-based copolymer by using the catalyst.