A mixed Lagrangian-Eulerian finite-difference scheme has been developed to study the time dependent advection and diffusion of air pollutants for variable emission rates, wind velocity and diffusion coefficients. The Lagrangian and Eulerian procedures are applied, respectively, to the advective and diffusive transport. The Lagrangian technique is mass conserving and completely avoids the artificial diffusion errors associated with conventional Eulerian finite-difference approximations. Furthermore, it does not require any condition of numerical stability. Compatibility with the Eulerian grid geometry is achieved by using a convergent approximation of the wind profile providing a translation of the concentration field to positions always coincident with grid points. The method is applied to the horizontal advection-vertical diffusion transport of line source pollutants. The diffusion is computed with an implicit finite-difference scheme allowing for a variable grid spacing. A Gaussian vertical distribution of the grid point “density” is chosen with its maximum at the source height. Typical numerical steady-state solutions obtained with different approximations of given velocity profiles are compared with corresponding analytical solutions.