PURPOSE: To prepare aluminoxane useful as a catalyst for olefin polymerization by mixing a water-contg. inert porous absorbent and an organoaluminum compd. and allowing water released from the absorbent to react with the compd.

CONSTITUTION: (A) An inert porous absorbent contg. 10-50 wt.% of water, such as fumed silica and aluminum hydroxide, (B) a trialkyl or triaryl aluminum compd., preferably a trialkyl aluminum compd. contg. a 1-8C alkyl part or a 6-10C aryl part, particularly trimethyl aluminum, and preferably (C) a solvent (such as heptane and toluene) are mixed in such weight rtios that C:B is 3:1-10:1, C:A is 4:1-10:1 and A:B is 1:2-2.5:1. Water released from A is allowed to react with B, to prepare the objective aluminoxane.