Abstract: The sound propagation characteristics of underwater steady-state vortex field are analyzed based on the ray acoustics theory. The ray differential equations in the two-dimensional steady-state vortex field are derived using the Eikonal equation in a moving medium. The receiving acoustic signal is obtained by the simulated ray trajectory of the sound wave passing through the vortex field. The mapping relationship between the phase of the received acoustic signal and the characteristic parameters of the vortex field is established rooted in the sound propagation characteristics of the vortex field. The characteristic parameters of the vortex field are inverted by numerical simulation with a relative error of less than 15% when compared to the theoretical value. The simulation results demonstrate the effective simulation of the phase change and sound ray trajectory, harnessing the advantages of intuitive visualization and efficient computation by ray acoustic theory. The numerical simulation also verifies that as the circulation of vortex increases, the impact of vortex on sound propagation becomes more pronounced. The characteristic parameters of the vortex field such as velocity distribution, vortex core position, and vortex circulation, can be estimated based on the phase change.