There are provided a process for producing a catalyst for -olefin polymerization, which comprises the step of contacting (1) a solid catalyst component having Ti, Mg and a halogen as essential components, (2) an organoaluminum compound and (3) a compound having a —C—O—C—O—C— bond group in a closed ring structure with one another; and a process for producing an -olefin polymer, which comprises the step of homopolymerizing or copolymerizing an -olefin in the presence of a catalyst for -olefin polymerization produced by the above process.