Most air pollutant dispersion models are analytical models that do not consider the spatial variation of wind velocity and diffusivity coefficient. To obtain an analytical model by considering the spatial variation of wind velocity and diffusivity coefficient, some simplifying assumptions must be made; in addition, the analytical solution is more complicated and less accurate. In this study, by solving the advection-dispersion equation for a steady and elevated pollutant stack, the spatial variation of the wind velocity and diffusivity coefficient is considered and the 2-dimensional distribution of the pollutant concentration is calculated. The model could be applied for both stable and unstable conditions. The advection-dispersion equation has been solved using the finite difference method. The proposed model has been validated using other researcher's experiments data and existing analytical models. The results show a good level of accuracy for the model.