The selective catalytic reduction (SCR) is perhaps the most efficient process to reduce nitrogen oxides (NOx) emissions in engine exhaust gas. Research efforts are currently devoted to realizing and tuning SCR-reactors for automotive applications to meet the severe future emission standards, such as the European “Euro VI”, in terms of NOx and particulate matter produced by vehicles. In this paper, we apply for the first time the Lattice Boltzmann Method (LBM) as a computational tool to study the performance of a SCR reactor. LBM has been recently adopted for the study of complex phenomena of technical interest, and it is characterized by a detailed reproduction of both the porous structure of SCR reactor and the fluid-dynamic and chemical phenomena that take place in it. The aim of our model is to predict the behavior and performances of SCR reactor by accounting for the physical and chemical interactions between exhaust gas flow and the reactor. Our results prove the reliability of our model as an accurate numerical tool for SCR performance prediction across physical space-scales.