Abstract: An efficient, accurate, and numerically stable coupled-mode solution for acoustic propagation in a rangedependent waveguide was presented. This method is numerically stable due to the appropriately normalized range solutions introduced in the formulation. In addition, by combining a forward marching and a backward marching, this method provides accurate solutions for range-dependent propagation problems, especially those characterized by large bottom slope angles and/or high impedance contrast between water and the bottom. Furthermore, this two-way solution also features in high efficiency, which is achieved by applying the single-scatter approximation. Numerical examples are also provided to demonstrate the efficiency, accuracy, and stability of this method.