Solid titanium catalyst component, catalyst for polymerization of olefin and process for producing olefin polymer

A solid titanium catalyst component (I), comprising titanium, magnesium, halogen, and a cyclic ester compound (a) represented by the following formula (1b):

• wherein n is an integer of 5 to 10;
• bonds between the carbon atoms in the cyclic backbone are all single bonds;
• a plurality of R1's are each independently a monovalent hydrocarbon group having 1 to 20 carbon atoms;
• a plurality of R's are each independently an atom or group selected from hydrogen atom, a hydrocarbon group having 1 to 20 carbon atoms, a halogen atom, a nitrogen-containing group, an oxygen-containing group, a phosphorus-containing group, a halogen-containing group and a silicon-containing group, and they may be bonded to each other to form a ring, but at least one of R's is not a hydrogen atom;
• and
• a double bond may be contained in the backbone of the ring formed by the bonding of R's, and in the case where two Ca's are contained in the backbone of the ring, the backbone of the ring have 5 to 10 carbon atoms.