This paper presents a new formulation of the 2D shallow water equations, based on which a numerical model (referred to as NewChan) is developed for simulating complex flows in nonuniform open channels. The new shallow water equations mathematically balance the flux and source terms and can be directly applied to predict flows over irregular bed topography without any necessity for a special numerical treatment of source terms. The balanced governing equations are solved on uniform Cartesian grids using a finite-volume Godunov-type scheme, enabling automatic capture of transcritical flows. A high-order numerical scheme is achieved using a second-order Runge–Kutta integration method. A very simple immersed boundary approach is used to deal with an irregular domain geometry. This method can be easily implemented in a Cartesian model and does not have any influence on computational efficiency. The numerical model is validated against several benchmark tests. The computed results are compared with analytical solutions, previously published predictions, and experimental measurements and excellent agreements are achieved.