The present invention provides a process for producing an α-olefin polymer comprising polymerizing or copolymerizing (a) C3 or higher α-olefin(s) in the presence of an olefin polymerization catalyst comprising solid titanium catalyst component (I) containing titanium, magnesium, halogen, and a compound with a specific structure having two or more ether linkages and organometallic catalyst component (II) with high catalytic activity. In this process, particularly even in (co)polymerizing (a) higher olefin(s), demineralization is unnecessary. A 4-methyl-1-pentene-based polymer obtained by polymerization using the catalyst of the present invention is excellent in tacticity, transparency, heat resistance, and releasability, and the polymer is particularly suitable for a release film.