Abstract: A coupled-mode formulation for acoustic propagation in range-dependent waveguides is presented in this paper. This method is capable of providing two-way solutions to two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry. The direct global matrix (DGM) approach is adopted in computing the coupled-mode coefficients in each segment, in order to eliminate accumulative errors in the traditional propagator matrix approach. In addition, appropriate normalized range solutions are introduced to avoid numerical overflow problems. Furthermore, closed-form expressions for coupling matrices are derived for ideal waveguides. Mode coupling in a waveguide involving a single stair step is analyzed. Numerical results for an ASA benchmark problem are also provided, which shows great agreement between the numerical solutions by this method and the analytical solutions. The numerical results indicate that the present method is numerically stable and accurate, and thus suitable for range-dependent problems.