This article presents a model that incorporates a continuum approach for the active sites to take account of the non-uniform activity of the Ziegler-Natta catalyst. The basic idea is that the activity may be considered as a continuous variable and thus the moment of live polymer is expressed as a distribution function with respect to the continuum index representing the activity. The site-average values of the moments of polymer are then obtained analytically to give a set of ordinary differential equations. When the quasi-steady state hypothesis is introduced for the live polymers, direct integration of the model equations gives rise to extremely simple expressions for the molecular weight averages. In particular, the polydispersity index may be predicted by identifying two distribution parameters for a specific polymerization system and is found to be independent of the hydrogen concentration. Application is illustrated by adapting the present model to experimental systems reported in the literature and thereby its validity is established.