This paper considers the mathematical model for solute transport in fractured media, sets up the discrete generalized difference scheme, gives numerical examples under different fractured media retardation coefficients and compares the numerical solution with analytic solution.Comparison results show that the solution of established generalized difference scheme to solute transport in fractured media is reliable, that this scheme is stable and practical and can be used to numerically simulate the physical process for the solute transport in more complex fractured media.