Abstract: The Runge-Kutta discontinuous Galerkin scheme(RKDG), which maintains balance of flux and source terms, is formulated to solve one-dimensional shallow water flows in non-prismatic channel. To validate the numerical model, a transcritical flow over a hump in a non-prismatic channel and a hydraulic jump were simulated. The simulated results from RKDG agree well with the analytical solution and measured values. It is shown that the RKDG scheme developed in the present paper has proven its capability of capturing sharp waveform in discontinuous flows.