The present invention relates to a catalyst component and a catalyst for olefin polymerization. The catalyst component utilizes magnesium halide and silica as composite support, and the particle morphology thereof can be improved by regulating the ratio of magnesium halide to silica. Further, the purpose of stabilizing the rate of catalytic polymerization reaction and improving the particle morphology of polymer so as to meet the requirements on catalyst performance of various polymerization processes can be achieved through the combination of the supports of the catalyst. In the meantime, when used in the polymerization of propylene, the catalyst of the present invention exhibits a relatively high polymerization activity and high stereospecificity.