The aim of this article is to present a complete and detailed gasification/smoldering model for a single biomass pellet. The four main objectives were: to write a modified one-dimensional numerical model using C++, to validate the results using experimental data from the literature, to present an overview of the one-dimensional model results, and to investigate the effects of main parameters used in the model. This model includes all the necessary partial differential equations describing continuity, species, energy and pressure. All the equations are highly coupled and are solved using a finite volume, central difference scheme. A time-marching procedure is based on a fully implicit scheme. Validations with air smoldering combustion are presented and the results show good agreement with the experimental data. The detailed results from this model show, for example, the temperature profile, the gas species distribution, the carbon content and the reaction rate. A discussion about the important parameters and their effects on this model is also presented. The parametric study shows that the devolatilization rate can prolong or shorten the duration of devolatilization stage but it cannot affect the highest temperature that the combustion can reach. As for the boundary condition for the temperature distribution, the radiation from the heating wall is a dominant factor to the temperature distribution within the pellet, whist the convection from the ambient flow has a negligible impact. A two-step and four-step hydrocarbon combustion scheme is implemented in this one-dimensional CFD model. The results show that, both schemes can predict the temperature quite well compared to the experimental data, with an error of up to 5% in the temperature simulation.