To prepare at a high yield a cocatalyst component useful for olefin polymerization by reacting a hydrocarbon compound solution containing a trialkylaluminum compound with water containing a small quantity of an aluminum compound.

A hydrocarbon compound solution containing 1-70 wt.% of trialkylaluminum compound is reacted with water containing 0.01-10 wt.% of an aluminum compound such as aluminum hydroxide, an aluminoxane, a trialkylaluminum or the like in a molar ratio of water/trialkylaluminum compound of (0.1-1.5):1 to give an aluminoxane. As the trialkylaluminum compound is preferable trimethylaluminum, triethylaluminum, triisobutylaluminum, trihexylaluminum, trioctylaluminum or a combination thereof. As the hydrocarbon compound is preferable a 5-12C linear or branched hydrocarbon or an aromatic hydrocarbon compound.