Summary: A depth-averaged two-dimensional model has been developed in the curvilinear coordinate system for free-surface flow problems. The nonlinear convective terms of the momentum equations are discretized based on the explicit-finite-analytic method with second-order accuracy in space and first-order accuracy in time. The other terms of the momentum equations, as well as the mass conservation equation, are discretized by the finite difference method. The discretized governing equations are solved in turn, and iteration at each time step is adopted to guarantee the numerical convergence. The new model has been applied to various flow situations, even for the cases with the presence of subcritical and supercritical flows simultaneously or sequentially. Comparisons between the numerical results and experimental data show that the proposed model is robust with satisfactory accuracy.