This paper simulates and analyzes numerically the dispersion characteristics of the waves propagating in the shallow-ocean overlying a semi-infinite elastic solid. The analytical solution of the acoustic field in the shallow-ocean, excited by an explosive point source in the solid bottom, is derived by using the theories for sound propagation in liquid and solid. The time-domain waveforms of transient acoustic field are simulated with the above analytical solution. The dispersion characteristics of the transient acoustic field are analyzed by using the smoothed pseudo Wigner-Ville distribution.