In this study, we investigate the effect of temperature reaction and hydrogen amount as the most effective process variables on Ziegler–Natta catalysts; with the aim of evaluating their effects on how to grow molecular weight and its dispersity during polypropylene polymerization with the aid of a validated mathematical model. The used approach in modeling is polymer moment balance technique (population balance approach) in MATLAB/SIMULINK environment, and then the model has been validated by experimental data come from a laboratory scale reactor. The main target of this study is to gain considerable insight into Ziegler–Natta catalyst performance against changing of the variables. The model might be applicable for the catalyst makers to evaluate and to improve their catalysts and also could be useful for process chemical engineers to easily operate the plant, to replace a new catalyst, to optimize process conditions and to generate new formulation for a new grade.