Abstract: Disclosed is a method for polymerization and copolymerization of olefin characterized by polymerizing or copolymerizing olefins in the presence of: (A) a prepolymerized catalyst obtained by prepolymerizing olefins in the presence of (a) a solid complex titanium catalyst prepared by the following steps, (b) an aluminum alkyl and halogenated aluminum, and (c) an electron donor, wherein the steps comprises: (i) preparing a magnesium compound solution by dissolving a magnesium halide compound into an oxygen-containing solvent mixture of a cyclic ether and one or more alcohols; (ii) preparing a carrier by firstly reacting the resulted magnesium compound solution with a titanium halide compound at ?10-30° C.