A two-dimensional numerical model was developed for simulating free surface flow. The model is based on the solutions of two-dimensional depth averaged Navier-Stokes equations. A finite volume method is applied such that mass conservation is satisfied both locally and globally. The model adopted the two-step, high resolution MUSCL-Hancock scheme. This Godunov type scheme is used together with the approximate Riemann solver. The boundary cells are treated as cut-cells in order to accommodate arbitrarily geometries of natural rivers. An automatic wet-cell cutting algorithm is incorporated into the model so that the wet areas cut out of the mesh have cut-cells representing their boundaries. There are sixteen types of cut-cells depending on the slope of the boundary intersection with the cell. A cell merging technique is incorporated in the model that combines small cells with neighboring cells to create a larger cell that helps satisfying the CFL condition. The cut-cells approach permits a fully boundary-fitted mesh without implementing a complex mesh generation procedure for irregular geometries. The model is verified by several laboratory experiments including unsteady flow passing through cylindrical piers and dam break flow in a rectangular channel.