Abstract: The discrete procedure of non-conservative St. Venant equations is carried out by making use of the flux difference splitting scheme. In order to maintain the same dispersed form, characteristic theory is introduced into boundary points discretization. Combining with entropy correction, the flux limiter is introduced into the discrete equations to preserve the property of total variation diminishing (TVD). Based on the implication of TVD, a one-dimensional (1-D) river network model is derived. The 1-D model is used to simulate water levels and discharges in a reach of Chengtong River. Results show that the model is able to handle trans-critical flow fields with large time steps. The model simulates well the water stage and the diversion ratio of bifurcation, indicating the model has practical values in flow simulations.