This paper presents results of modeling of the passive contaminant diffusion from a continuous line finite-size source located on the underlying surface of a neutral near-ground atmospheric layer obtained by using the non-local two-parameteric turbulence model and the transport equation of mean concentration. In the proposed diffusion model the turbulent diffusion coefficient changes not only with the vertical coordinate but also with the distance downstream from the source according to the experimental data. The results of the modeling reproduce structural features of the concentration field.