Disclosed are a catalyst component and a catalyst for olefin polymerization, and an olefin polymerization method. The catalyst component comprises magnesium, titanium, a halogen and an internal electron donor, wherein the internal electron donor comprises a monocarboxylic acid ester compound and a diether compound, and the molar ratio of the monocarboxylic acid ester compound to the diether compound is (0.0035-0.7):1. By using the catalyst, a polymer having both a high isotactic index and a high melt flow index can be prepared.