In this study, the upwind McCormack scheme is introduced to combine the advantage of McCormack scheme, the second order accuracy and simplicity, and the advantage of the upwind scheme, to be applied to the discontinuous flows. This scheme also has another advantage of treating the source terms effectively. This model is approved through applying to the discontinuous flow case with the analytical solution, and the natural river with very strong source terms. Applications of the upwind McCormack scheme developed in this paper show good agreements with the analytical solution without numerical oscillation in existing McCormack scheme. Futhermore, applications to the natural river, the lower Han river with strong variation of bed and width, also show good results in case of both steady flow and unsteady flow. The upwind McCormack scheme in this study will be used for the analysis of flow in natural rivers effectively.