This work presents an analytical solution for the transient three-dimensional advection-diffusion equation. This solution, obtained from a combination of the variable separation method and GILTT (Generalized Integral Laplace Transform Technique) is used to simulate the pollutant dispersion in the atmosphere. The new solution has the advantage of not requiring a numerical inversion performed in the temporal variable in works using only GILTT technique. The model was tested in low wind condition, with diffusion in transverse and longitudinal directions and stochastic speeds. Simulations were performed for the INEL experiment. The analytical character of the model makes it simple, which represents advantages in its development and implementation, as well as in the computational cost for execution.