In this study most of the Lagrangian similarity relations are reviewed. The problem of modelling contaminant dispersion from ground-level sources in low wind for unstable and stable conditions is investigated. The present study proposes a steady-state mathematical model for dispersion of contaminants in low winds that takes into account the along-wind diffusion. The novel aspect is that the solution of the advection–diffusion equation for these conditions is obtained by applying the Laplace transform. Considering the planetary boundary layer as a multilayer system, we assume that the height of the planetary boundary layer "h" is discretizing stepwise into N sub-intervals. The wind speed is used as a function in the logarithmic form, and the eddy diffusivities are functions of the vertical distance “z,” which represents the near-source diffusion in weak winds. The performances of the model were evaluated against the field experiments carried out at the Prairie-Grass experiment of Sulphur Dioxide during the stable and unstable conditions in the United States of America. It was found that, the most proposed data are located within a factor of two with already existing observed concentrations data. The proposed model was in good agreement with already existing observed concentrations data in unstable and stable conditions. The proposed model achieved 100% and 82% from observed data of prairie grass in unstable and stable conditions, respectively. The study demonstrates the effectiveness of the proposed model in predicting pollutant dispersion with high accuracy.