A hybrid approach that combines the method of moments and Monte Carlo simulation to predict the molecular weight distribution of low-density polyethylene for a continuous stirred tank reactor system is proposed. A ‘Block’, which is repeating reaction group, is introduced for the calculation cost-effective simulation. This model called the ‘block Kinetic Monte Carlo’ is ~10 to 32 times faster than Neuhaus’s model. The model can be applied to any steady state system and provide a calculation cost reduction effect, where one reaction is much faster than others, for example, the propagation reaction. Furthermore, we performed a case study on the effects of the system temperature and initiator concentration on the MWD and reaction rate ratio. Based on the simulation results of 180 case studies, we determined a quantitative guideline for the appearance of shoulder, which is a function of the rate ratio of reactions to the propagation reaction.