A numerical model using the finite-element and finite-volume methods is developed for the resolution of two-dimensional free-surface how equations including air entrainment and applied to calculation of the flow in a spillway. The model is implemented on an unstructured triangular mesh where the standard Galerkin scheme and an upwind finite-volume scheme are developed to solve the continuity and the conservative momentum equations, respectively. The time integration is performed using the fourth-order-accurate Runge-Kutta method with time steps that satisfy the Courant-Friedrichs-Lewy condition. An artificial dispersion term is introduced to eliminate spurious oscillations. A test problem in a spillway is solved to verify the applicability of the model to practical design. A physically realistic solution is obtained that represents a series of flow state alternations from supercritical to subcritical and vice versa, as well as the surface level increase due to the entrained air. The temporal mean of the calculated solution is compared with experimental temporal mean data and examined by posteriorly evaluating the residual term due to vertical nonhomogeneity of velocity. The investigations prove that the model is valid as a primary analysis tool for hydraulic design of spillways.