Abstract: The sound field of an underwater moving source in the Pekeris waveguide environment is studied in this paper. A numerically stable wavenumber integration solution and the one-dimensional approximate wavenumber integration method are applied to solving the sound field of a moving source in the Pekeris waveguide. The twodimensional wavenumber integral expression of the moving source is deduced, and the one-dimensional approximate solution is given. A numerically stable calculation method is introduced in the calculation of the depth Green's function. In the simulation experiment, the accurateness of the one-dimensional approximate wavenumber integration method is first verified under free space conditions. Combined with the numerically stable wavenumber integration method in the Pekeris waveguide, the sound field characteristics of a moving point source are simulated and analyzed.The frequency broadening and frequency shifting characteristics of the sound field of the moving source in the Pekeris waveguide are investigated by changing the waveguide and the source and receiver conditions.