Disclosed is an olefin polymerization catalyst comprising: a transition metal compound comprising one transition metal selected from the group consisting of Ti, Zr and Hf, and at least two ligands, wherein one ligand is a group having a cyclopentadienyl skeleton, and the remaining at least one ligand is a monovalent, bidentate, anionic chelating ligand having two coordinating atoms each coordinated to the transition metal, one of which atoms is selected from the group consisting of O, S, Se and Te, and the other of which atoms is selected from the group consisting of N, S, Se and Te, and wherein one of the remaining at least one ligand is optionally bonded to the group having a cyclopentadienyl skeleton through a bridging group. Also disclosed is a method for efficiently producing an olefin homopolymer or olefin copolymer by using this catalyst. By polymerizing an olefin using the olefin polymerization catalyst of the present invention, there can be advantageously produced an olefin homopolymer having a narrow molecular weight distribution or an olefin copolymer having not only a narrow molecular weight distribution but also a uniform copolymerization distribution. The produced polymer has high impact strength, high resistance to stress cracking, high transparency, excellent heat sealing properties at low temperatures, high blocking resistance, low tackiness, low extractability and the like.