A solid titanium catalyst component (I) of the present invention is characterized in that it contains titanium, magnesium, halogen, and a cyclic ester compound (a) represented by the following formula (1): ##STR00001## wherein n is an integer of 5 to 10; R.sup.2 and R.sup.3 are each independently COOR.sup.1 or R, and at least one of R.sup.2 and R.sup.3 is COOR.sup.1; a single bond (excluding C.sup.a--C.sup.a bonds, and a C.sup.a--C.sup.b bond in the case where R.sup.3 is R) in the cyclic backbone may be replaced with a double bond; a plurality of R.sup.1's are each independently a monovalent hydrocarbon group having 1 to 20 carbon atoms; and a plurality of R's are each independently a hydrogen atom or a substituent, but at least one of R's is not a hydrogen atom. When using this solid titanium catalyst component (I), an olefin polymer having a broad molecular weight distribution can be produced.