The present invention relates to a nitrogen heterocyclic carbene rare earth complex, a catalyst system which consists of the present invention, aluminum alkyl and an organoboron salt can catalyse the isoprene to carry out the solution polymerization, so as to prepare the polyisoprene with the crystallization property, high 3, 4-structure and high glass transition temperature (Tg). The molar ratio of aluminum alkyl and the rare earth complex is within the scope of 1 to 100, the molar ratio of the organoboron salt and the rare earth complex is within the scope of 0.5 to 2.0; the solvent which is used for polymerization can be toluene, bromobenzene, n-hexane, dichloromethane or chlorobenzene; the polymerization temperature range is -20 DEG C to 80 DEG C, the reaction time of polymerization at minus 20 DEG C is 36 hours, the reaction time of polymerization at 80 DEG C is 1 hour, and the monomer conversion rate can be up to 100 percent. The reaction is characterized by active polymerization, the molecular weight of the product can be controlled by the molar ratio of the monomer and the catalyst, the molecular weight of the polyisoprene can achieve 360,000 at most, and the glass transition temperature Tg is equal to 5 DEG C to 50 DEG C. The content of the 3, 4 structure of the polyisoprene is affected by the spatial effect and the electronic effect of the rare earth complex, the solvent type for polymerization reaction and the polymerization reaction temperature and so on, which is changed between 76 percent and 99 percent.