To provide an olefin polymerization catalyst capable of being easily synthesized for industrial use, and having very high polymerization activity by using only a very little amount of an activator, and a method for manufacturing an olefin polymer.

This catalyst for olefin polymerization comprises a transition metal component (A) and an activator (B), and the transition metal component is represented by formula (1) (wherein M is a transition metal of group 5 in the periodic table; X1, X2, and X3 may be the same or different and are each a 1-20C alkyl group, aryl group, aralkyl group or a halogen; R1, R2, and R3 may be the same or different and are each hydrogen, a halogen, or a 1-20C alkyl group, aryl group, or aralkyl group; and m is an integer of 0-3) and the activator (B) is a halogenated aluminum compound.