A production process of an α-olefin polymerization catalyst, comprising the steps of (1) reducing a titanium compound represented by a defined formula with an organomagnesium compound in the presence of an Si—O bond-containing silicon compound, (2) contacting the resultant solid catalyst component precursor, a halogenating compound and an internal electron donor with one another, and (3) contacting the resultant solid catalyst component, an organoaluminum compound and a Si-containing external electron donor represented by a defined formula with one another; and a production process of an olefin polymer using the above catalyst.