Process for producing olefin polymer and solid titanium catalyst component

A process for producing an olefin polymer is characterized in that it comprises polymerizing an olefin having 3 or more carbon atoms in the presence of a catalyst for olefin polymerization containing a solid titanium catalyst component (I) which contains titanium, magnesium, halogen, and a cyclic ester compound (a) represented by the following formula (1): wherein n is an integer of 5 to 10; R and R are each independently COOR or a hydrogen atom, and at least one of R and R is COOR ; and R s are each independently a monovalent hydrocarbon group having 1 to 20 carbon atoms, a single bond (excluding Ca-Ca bonds, and a Ca-Cb bond in the case where R is a hydrogen atom) in the cyclic backbone may be replaced with a double bond; and an organometallic compound catalyst component (II), at an internal pressure of the polymerization vessel which is 0.25 times or more as high as the saturation vapor pressure of the olefin at a polymerization temperature. According to this process, an olefin polymer having a broad molecular weight distribution can be prepared.