The present invention provides an olefin polymerization catalyst, which is free of polyfunctional aromatic compounds and has a large particle diameter, and a solid titanium component (I) which forms the catalyst. The olefin polymerization catalyst comprises a solid titanium component (I), an organometallic compound (II) and optionally an electron donor (III) wherein the solid titanium component (I) comprising titanium, magnesium and halogen is obtainable by allowing a magnesium compound (A) having no reducing ability in a liquid state to contact with an ester compound (B) represented by the following formula (1) and a liquid titanium compound (C) in a specific order, wherein R2 and R3 are COOR1 or R, and at least one of R2 and R3 is COOR1, two or more R1 each are a monovalent hydrocarbon group having 1 to 20 carbon atoms, and two or more R are a hydrogen atom, or a hydrocarbon group having 1 to 20 carbon atoms, and at least two of Rs may be bonded each other to form a ring, and the skeleton of the ring formed may include a double bond or a hetero atom.