This article deals with the development of a model for the polymerization process using a Ziegler-Natta catalyst in a slurry reactor system. Employed here is the hierarchical model describing the entire reactor system that is subcategoried by the gas bubble phase, the continuous gas phase, the liquid phase, the solid polymer particle, and the surface of catalyst where chemical reaction occurs. The concept of the multigrain model (MGM) is introduced to describe the growth of polymer particle from the original catalyst particle. We also adopt the concept of multiple active sites to elucidate the broad molecular weight distribution (MWD). The major concern here is the effects of the hydrogen concentration and the size of the initial catalyst on the performance of the polymerization reactor. It is demonstrated that the hydrogen gas can be used for the purpose of controlling not only the molecular weight but the molecular weight distribution (MWD) of the polymer. In addition, the relationship between the molecular weight and the concentration of hydrogen gas is investigated. The size of the initial catalyst is found to exercise a significant influence on the morphology of the resultant polymer particle.