A catalyst component for use in the polymerization or copolymerization of olefin(s) is obtained by contacting the following components (1) to (4) with one another:
(1) a compound of the general formula Me¹R¹p(OR²)qX¹4-p-q where R¹ is a hydrocarbon radical having 1 to 24 carbon atoms, X¹ is a halogen atom, Me¹ is Zr, Ti or Hf, and n is 0 ≦ n ≦ 4; (2) a compound of the general formula Me²R³m(OR⁴)nX²z-m-n where R² is a hydrocarbon radical having 1 to 24 carbon atoms, X² is a halogen atom, Me² is an element from Groups I to III in the Periodic Table, z is the valence of Me² and m is 0 ≦ m ≦ z; (3) an organocyclic compound having two or more conjugated double bonds; and (4) a modified organoaluminum compound containing Al-O-Al bond and with at least one branched-chain alkyl group being attached to aluminum atom.