Hydrogen is considered as an essential fuel of the future, which can reduce the reliance on oil. It can be produced via the various chemical process including ion exchange membranes, biomass gasification, steam reforming. The use of biomass as alternative energy for fossil fuels has been attracting attention recently due to the rapid depletion of fossil fuel sources and the costly price tag of crude. However, one of the critical challenges in biomass gasification technology is the removal of tar, which contains oxygenated hydrocarbons and aromatic hydrocarbons which are difficult to degrade and can lead to a decrease in efficiency of the process operations and an increase in maintenance and operating costs. The steam reform is a widely known technique for the removal of tar, avoiding equipment damage, and can produce hydrogen fuel that is a relevant alternative for reducing environmental impact. In this sense, this paper presents a numerical analysis of the steam reforming using toluene as a model compound to produce hydrogen in a fixed bed catalytic reactor. The main objective of this paper was the development of a dynamic mathematical model to study non-isothermal steam reforming of toluene in a catalytic reactor. This model is described by a system of Partial Differential Equations (PDEs). Also, to solve these PDEs, it was using the technique Coupled Integral Equation Approach (CIEA) and with a code in FORTRAN 95 language that allowed obtaining data about the temperature profiles and H2 production.