This work studies the use of the Progressive Diffusion Reaction Model (PDRM) in modelling the graft polymerization of 4 – Chloromethylstyrene unto irradiated polyethylene substrates. The graft polymerization process being modelled is the active step in the synthesis of a novel polymer-based catalyst for biodiesel production. Experimental data for the graft polymerization process and certain process data needed for the modelling were obtained/evaluated from literature. The PDRM was derived from material balance equations on a spherical particle with a hypothetical reaction hold-up. The R2 and t-Test values between experimental and model generated data were investigated for model validity with an R2 value > 0.85 and t-Test value > 0.05 considered as the criteria for validity. The PDRM gave R2 values greater than 0.85 and t-Test values greater than 0.05 at temperatures of 40oC, 50oC and 60oC for polyethylene samples with irradiation dosages of 20kGy, 30kGy, 40kGy and 50kGy respectively. The model was applied in generating concentration data for the grafting process at shorter time intervals and at process conditions not experimented upon. The PDRM proved valid for modelling the grafting process at the various temperatures and irradiation doses and is recommended for modelling other such operations.