To provide an addition polymerization catalyst component and an addition polymerization catalyst, used in manufacturing an addition polymer high in melt tension and excellent in processability; and to provide a method for manufacturing an addition polymer high in melt tension and excellent in processability.

The polymerization catalyst for ethylene and α-olefin is prepared by bringing an olefin polymerization catalyst component including a transition metal compound of (i) and a transition metal compound of (ii) into contact with an activating cocatalyst component and an organoaluminum compound: (i) A transition metal compound which has two groups having a cyclopentadienic anion skeleton, the two groups being bonded to each other directly or through a crosslinking group, and has hafnium as a central metal; (ii) A transition metal compound which has two groups having a cyclopentadienic anion skeleton having a substituent, the two groups not being bonded to each other, and has zirconium as a central metal.