Diffusion of passive admixtures from a continuously operating limited-size source, situated on the underlying surface of the neutral atmospheric surface layer, is simulated based on a non-local two-parameter model of turbulence and the equation of transport for the mean concentration. In the proposed diffusion model, the coefficient of turbulent diffusion varies not only with altitude, but also with the distance from the source in the downstream direction according to the data of laboratory measurements [J.E. Fackrell and A.G. Robins, J. Fluid Mech., No. 117, 1-26 (1982); M. Porch and J.E. Cermak, J. Heat Mass Transfer, No. 7, 1083-1095 (1964)]. The results of simulation agree with the measured data on structural peculiarities in transformation of the concentration field.