Recent studies have illustrated that the Multichannel Analysis of Surface Waves (MASW) method is an effective geoacoustic parameter inversion tool. This particular tool employs the dispersion property of broadband Scholte-type surface wave signals, which propagate along the interface between the sea water and seafloor. It is of critical importance to establish the theoretical Scholte wave dispersion curve computation model. In this typical study, the stiffness matrix method is introduced to compute the phase speed of the Scholte wave in a layered ocean environment with an elastic bottom. By computing the phase velocity in environments with a typical complexly varying seabed, it is observed that the coupling phenomenon occurs among Scholte waves corresponding to the fundamental mode and the first higher-order mode for the model with a low shear-velocity layer. Afterwards, few differences are highlighted, which should be taken into consideration while applying the MASW method in the seabed. Finally, based on the ingeniously developed nonlinear Bayesian inversion theory, the seafloor shear wave velocity profile in the southern Yellow Sea of China is inverted by employing multi-order Scholte wave dispersion curves. These inversion results illustrate that the shear wave speed is below 700 m/s in the upper layers of bottom sediments. Due to the alternation of argillaceous layers and sandy layers in the experimental area, there are several low-shear-wave-velocity layers in the inversion profile.