Abstract: A solid titanium catalyst component comprising (a) magnesium, (b) titanium, (c) a halogen, (d) a polyether, (e) a hydrocarbon and (f) an electron donor other than the polyether (d) as essential components is provided. Also a process for preparing a solid titanium catalyst component for olefin polymerization, comprising the steps of contacting a halogenated magnesium compound with a compound selected from the group consisting of an alcohol, an ether and an ester in a hydrocarbon solvent to obtain a magnesium compound solution, contacting the magnesium compound solution with a polyether and contacting the resultant solution with a liquid titanium compound is provided. Further, a catalyst for olefin polymerization comprising the above-mentioned solid titanium catalyst component, an organoaluminum compound catalyst component and an electron donor, and a process for polymerizing an olefin using the catalyst for olefin polymerization are also disclosed.