Analytical models are indispensable tools to study the ad-hoc problems connected with the severe impacts of harmful air pollutants. The analytical models based on the solution of the advection-diffusion equation have been the first and remain the convenient way for modeling air pollutant dispersion as it is easy to handle the dispersion parameters and related physics in it. A semi- mathematical model describing the crosswind integrated concentration is presented. The analytical solution to the resulting advection-diffusion equation is limited to constant and simple profiles of eddy diffusivity and wind speed. In practice, the wind speed depends on the vertical height above the ground and eddy diffusivity profiles on the downwind distance from the source as well as the vertical height in the short-range dispersion. In the present model, a method of eigenfunction expansion is used to solve the resulting partial differential equation with the appropriate boundary conditions. This leads to a system of first-order ordinary differential equations with a coefficient matrix depending on the downwind distance. An approach based on Taylor’s series expansion is introduced to find the numerical solution of the resulting first order system. The method is applied to various profiles of wind speed and eddy diffusivities. The solution computed from the proposed methodology is found to be efficient and accurate in comparison to those available in the literature. The solution derived is used to deduce the concentration distribution at all the points in the domain by assuming a Gaussian distribution in the crosswind direction. The performance of the model is evaluated with the diffusion datasets from Prairie Grass experiment in various stability classes varying from very unstable to neutral and stable conditions. In addition, it is evaluated using low wind diffusion data taken from Idaho experiments in stable conditions.