Biomass gasification is regarded as one of the most promising energy recovery technologies for the widespread use of biomass. Mathematical models have been developed to understand this process in downdraft fixed beds using zero- and one-dimensional models, but only a limited number of two-dimensional (2D) models for downdraft fixed-bed reactors can be found in the literature. In this study, a 2D computational fluid dynamics (CFD) model was developed to study the gasification process in a downdraft configuration, considering drying, pyrolysis, combustion, and gasification reactions. The gas and solid phases were resolved using an Euler-Euler multiphase approach, with exchange terms for the momentum, mass, and energy. The standard k-epsilon turbulence model was used in the gas phase. The model results were compared to existing data from a demonstration-scale fixed-bed downdraft gasifier. The simulation results exhibit a reasonable agreement with the experimental data. Parameter studies were performed on the basis of the developed model, which indicated that an external heat source for the high-temperature agent gasification (HTAG) technology using superheated air combined with steam resulted in a limited combustion need in the gasifier and produced syngas with a high H-2 fraction and low tar content, which is environmentally preferable.