This paper presents the catalytic pyrolysis of a constant-composition mixture of zeolite β and polyethylene terephthalate (PET) polymer by thermogravimetric analysis (TGA) at different heating rates (2, 5, 10, and 20 K/min). The thermograms showed only one main reaction and shifted to higher temperatures with increasing heating rate. In addition, at constant heating rate, they moved to lower temperatures of pure PET pyrolysis when a catalyst was added. Four isoconversional models, namely, Kissinger–Akahira–Sunose (KAS), Friedman, Flynn–Wall–Qzawa (FWO), and Starink, were applied to obtain the activation energy (Ea). Values of Ea acquired by these models were very close to each other with average value of Ea = 154.0 kJ/mol, which was much lower than that for pure PET pyrolysis. The Coats–Redfern and Criado methods were employed to set the most convenient solid-state reaction mechanism. These methods revealed that the experimental data matched those obtained by different mechanisms depending on the heating rate. Values of Ea obtained by these two models were within the average values of 157 kJ/mol. An artificial neural network (ANN) was utilized to predict the remaining weight fraction using two input variables (temperature and heating rate). The results proved that ANN could predict the experimental value very efficiently (R2 > 0.999) even with new data.