A novel catalytic membrane was prepared from polysulfone powders covalently linked with acidic ionic liquids (PSF-ILs), as a heterogeneous catalyst to produce reducing sugar for biomass inulin hydrolysis in a catalytic membrane reactor. However, a complete kinetic model describing the relationship between catalyst physical properties and hydrolysis performance is lacking. The present work attempts to build a hydrolysis kinetic model for the relationship between the conversion and the structure of the PSF-ILs membrane (such as membrane thickness, pore size, porosity and specific surface area). The reaction parameters, such as the reaction time, reaction temperature as well as the nature of the catalyst were of crucial importance in terms of optimal conversion of the biomass inulin to reducing sugar or platform chemicals. The results showed that the structure of the PSF-ILs membrane has a significant effect on its catalytic performance. The PSF-ILs membrane with the best catalytic performance was selected and the maximum TRS yields were up to 100% after two rounds of inulin hydrolysis. The conversions obtained from the established model are in good agreement with the experimental data. Understanding the structure–property relationship of the PSF-ILs membrane will be helpful in designing the physical structure of the membrane to improve its catalytic activity and reusability. Therefore, it is a type of green catalyst with potential application prospects in many catalysis fields.