An olefin polymerization catalyst and preparation method and use thereof are provided. The catalyst component comprises (1) an active magnesium halide, (2) a titanium compound containing at least one Ti-halide bond supported thereon, and (3) an electron donor selected from the group consisting of one or more sulfonyl-containing compounds having the following formula. There are two methods for preparing such solid catalyst component: I) treating the active magnesium halide (1) particles with alkylaluminum, subsequently adding the electron donor (3), treating it with the solution of titanium compound (2) one or more times; II) adding spherical magnesium chloride alcoholate particles to the solution of titanium compound (2), subsequently adding the electron donor (3), treating it with the solution of titanium compound (2) one or more times. The catalyst system comprises such solid catalyst component, a co-catalyst (alkylaluminum compound) and an external electron donor.