This paper presents a one-dimensional steady state mathematical model for the simulation of a small scale fixed-bed gasifier. The model is based on a set of differential equations describing the entire gasification process of softwood pellets and is solved by a two step iterative method. The main features of the model are: homogeneous and heterogeneous combustion and gasification reactions, one-step global pyrolysis kinetics and drying, heat and mass transfer in the solid and gas phases as well as between phases, heat loss, particle movement and shrinkage within the bed. The pyrolysis model has been improved by partially cracking primary tar into lighter gases according to experimental data. The model is used to simulate a laboratory scale fixed-bed updraft gasifier. Good agreement is achieved between prediction and measurements for the axial temperature profiles and the composition of the producer gas. Moreover, results are presented for different air to fuel ratios and varying power inputs. The gasification process is improved by increasing the power input of the gasifier as a result of higher temperatures. Furthermore, a higher air to fuel ratio lowers the efficiency of the gasification process.