A new numerical method for nonideal transport of solutes in porous media is developed by first using the Laplace transform to eliminate the time dependency and then the streamline upwind scheme to solve the spatial equations. The transient solution is ultimately recovered by an efficient quotient difference inversion algorithm. By introducing complex-valued artificial dispersion in the weighting functions, characteristics of the transient solutions have been successfully addressed. The optimum of the complex-valued artificial dispersion has been derived for one-dimensional problems. In multidimensional cases the streamline upwind scheme is modified by adding complex-valued artificial dispersion along the streamline. Within this numerical scheme the grid orientation problems have been successfully treated. The limitations on the cell Peclet number and on the Courant number were greatly relaxed. Both one-dimensional and two-dimensional numerical examples are used to illustrate applications of this technique. ¿ American Geophysical Union 1995.