This paper is concerned with a high-resolution mathematical model for one-dimensional (1D) hydraulic jump flows. The 1D shallow water equations of Saint-Venant were solved with the essentially non-oscillatory (ENO) scheme, the finite volume method (FVM) and the total variation diminishing (TVD) Runge-Kutta-type method. This model was used to predict the hydraulic jump flows, and the numerical resolutions are in agreement with the experimental ones, which indicate that this model is fairly effective and accurate for simulating hydraulic jump flows.