This paper is concerned with a mathematical model for numerical simulation of 1D discontinuous flow problems. The governing water equations are solved by an implicit bi-diagonal numerical scheme, based on the MacCormack’s predictor-corrector technique, and the oscillations near the vicinity of discontinuity/shocks are smoothed by a proposed technique. The mathematical model was used to numerically compute the water surface from supercritical flow to subcritical one or from subcritical flow to supercritical one in a rectangular open channel, and was also used to predict 1D wave due to an instantaneous opening of sluice gate problem in a rectangular open channel, and their results are in agreement with the theoretical results, which shows that the proposed method is accurate, reliable and effective in simulation of discontinuous flow problems