Most studies have been conducted in batch reactors. Therefore, understanding the catalytic reaction kinetics and mass transfer in continuous catalytic reactors is essential for the design of heterogeneous catalysts and optimisation of catalytic degradation processes in heterogeneous systems. In this research, granular catalysts (Co-600/AlSi-0.25/AP) is used to investigate the kinetic constants and mass transfer resistance for the continuous catalytic decomposition of peroxymonosulfate (PMS) and degradation of p-nitrophenol (PNP) in a fixed bed reactor. The flow rate is 5 mL/min and reaction temperature is 30 °C, intrinsic kinetic constants of PMS decomposition and PNP degradation are 48 and 195 kg−1·min−1·L, respectively, which are 20–30 times of the apparent kinetic constants of PMS decomposition and PNP degradation in fixed bed reactors, respectively. The decomposition rates of PMS and PNP are controlled by mass transfer, and the reaction takes place in the diffusion-controlled regime. The mass transfer kinetic model based on the plug-flow model shows a good agreement between the calculated data and the experimental data. Which indicate that PMS decomposition and pollutant degradation in a fixed-bed reactor can be predicted by mass transfer kinetic modelling, guide the design of catalysts and the optimisation of heterogeneous catalytic reaction system in a fixed-bed reactor.