An operotor-spliting method for the two-dimensional transport equation is developed. In the convection phase, a Galerkin weighted residual approach is employed to minimize the error generated by interpolation. Computer execution time is reduced by adopting Simpson's rule for some of the numerical integrations and by using an iteration stategy in the dispersion phase, thus avoiding the matrix inversion procedure in each time step. Several numerical examples are presented. The numerical results are coincident with the exact analytical solutions.