In this paper, a well-balanced finite difference weighted essentially non-oscillatory scheme is presented for modeling transport and diffusion of pollutant in shallow water flows. The scheme balances exactly the flux gradients and the source terms. Extensive one-dimensional and two-dimensional numerical experiments on uniform and curvilinear meshes strongly suggest that high resolution results are achieved for both water depth and pollutant concentration. The scheme is efficient and robust and can be applied to practical numerical simulation of pollutant transport phenomena in shallow water flows. Copyright © 2012 John Wiley & Sons, Ltd.