PURPOSE: To obtain the subject catalyst consisting of specific transition metal compound(s), excellent in polymer yield, capable of obtaining high-molecular weight olefinic polymers of high bulk density, high in stability under polymerization conditions, capable of controlling the molecular weight distribution of the aiming polymers through hydrogenation and of reducing the use of cocatalyst.

CONSTITUTION: This new catalyst consists of at least one kind of transition metal compound selected from those of formula I or II (M is 3A, 4A, 5A, 6A, 7A or 8 group transition metal including lanthanide series; X is an anionic ligand; (n) is an integer obtained by subtracting 2 from the number of groups (G) in the Periodic Table; L1 and L2 are ligands which may be mutually crosslinked; J is a non-ligand anion). The combination of L1 and L2 is as follows: (1) L1 is a tridentate ligand and L2 is ligand having σ-bond or σ-plus π-bond, or (2) L1 is a pentadentate ligand having heterocyclic five-membered ring and L2 is ligand having σ-bond or σ-plus π-bond (or at least one lone electron pair- donating bond).