The subject of this work is the mathematical modelling of a counter-current moving-bed gasifier fuelled by wood-pellets. Two versions of the model have been developed: the one-dimensional (1D) version-solving a set of Ordinary Differential Equations along the gasifier height-and the three-dimensional (3D) version where the balanced equations are solved using Computational Fluid Dynamics. Unique procedures have been developed to provide unconditionally stable solutions and remove difficulties occurring by using conventional numerical methods for modelling counter-current reactors.The procedures reduce the uncertainties introduced by other mathematical approaches, and they open up the possibility of straightforward application to more complex software, including commercial CFD packages. Previous models of Hobbs et al., Di Blasi and Mandl et al. used a correction factor to tune calculated temperatures to measured values. In this work, the factor is not required. Using the 1D model, the Mandl et al. 16.6 kW gasifier was scaled to 9.5 MW input; the 89% cold-gas efficiency, observed at 16.6 kW input, decreases only slightly to 84% at the 9.5 MW scale.