The invention provides a rare-earth catalyst of a nitrogen-containing heterocyclic carbene ligand and an olefin polymerization catalyzing method of the rare-earth catalyst. The rare-earth catalyst comprises a part A and a part B, wherein the part A is nitrogen-containing heterocyclic carbene coordinated rare-earth complex LMR2X, L is a cyclopentadienyl ligand selected from a cyclopentadienyl ligand, an indenyl ligand and a fluorenyl ligand, X is the nitrogen-containing heterocyclic carbene ligand selected from imidazolyl carbene, imidazolinyl carbene, triazolyl carbene and thiazolyl carbene, M is rare-earth metal selected from Sc, Y, Lu, Gd, Sm and Nd, and R is alkyl directly connected with the rare-earth metal; the part B is organoboron reagents. By using the rare-earth catalyst of the nitrogen-containing heterocyclic carbene ligand, the chain transfer reaction of propylene monomers can be effectively inhibited so as to prepare the homopolymer and copolymer, with higher molecular weight and narrower molecular distribution, of the propylene monomers.