The aluminoxane is obtained by bringing an organoaluminum compound into contact with a condensation agent, and includes a chain aluminoxane represented by the general formula (V) ##STR3## wherein R6 is an alkyl group having 1 to 20 carbon atoms, is preferably a methyl group and p is a number from 0 to 50, preferably 5 to 30; and a cyclic aluminoxane represented by the general formula (VI) ##STR4##