An isoprene or butadiene cis 1,4-selective polymerization catalyst system together with its polymerization method is provided. This catalyst system is composed of NCN-imine pincer type rare earth metal complex of formula [2,6-(CH═N—R1)2-4-R2-1-C6H2]LnX2(THF)n and alkylating reagent. In an hydrocarbon solvent or under bulk conditions, at a polymerization temperature in a range of −20-120° C., the conjugated diene is polymerized by using the catalyst system, to produce polyisoprene and polybutadiene having controllable number-average molecular weight, molecular weight distribution of 3.0 or less than, and cis 1,4-content of 95% or more, even 99% or more. The crude rubber and vulcanized rubber of the polyisoprene have high strength, stretching crystallization capability and transparency.