The present invention relates to a catalyst component suitable for olefin (co)polymerization, which comprises an aluminoxane supported on magnesium halide and contains more than 5% by weight of aluminum. The catalyst component according to the present invention is obtained by contacting an aluminoxane compound and a magnesium compound in the presence of a multifunctional organic compound. The catalyst comprising said component and metallocene shows good activity and consumes less amount of aluminoxane in the process of olefin polymerization. The polymer prepared by using said catalyst has an improved particle morphology and a narrow particle distribution.