Abstract: An unconditionally stable computation method based on the wave-number integration method is presented for the acoustics field excited by a line source in a Pekeris waveguide. Both up and down going waves in the depth-dependent wave equation are appropriately normalized in order to obtain a stable coefficient matrix. Analytical solution to the depth-dependent Green's function is also presented. Modal expansion of the Green's function is performed to validate the analytical solution. It indicates that the analytical solution is accurate. The transmission loss calculated by this method is compared with those given by KRAKENC with an example. It shows that when a certain mode is close to the bottom wavenumber, KRAKENC fails to find this mode. As a result, the field result by KRAKENC is inaccurate. However, the wavenumber-integration method suits well for such problems. Numerical results indicate that the present model can serve as a benchmark model for the problem of sound propagation excited by a line source in a Pekeris waveguide.