In marine exploration, velocity modeling of complex deep-water salt is an extremely challenging task. On the one hand, complex salt structures exist in a unique environment where seawater coexists with elastic media; on the other hand, the strong amplitude converted waves generated by high-velocity complex salt can affect the accuracy of traditional acoustic velocity modeling. Therefore, it is essential to fully consider these critical factors in order to carry out P- and S-wave velocity waveform inversion modeling for such special structures. Addressing the challenges faced in velocity modeling of complex deep-water salt using towed streamer data, this paper employs a method of boundary coupling between acoustic and elastic wave equations to construct an acoustic-elastic coupled equation (AECE). This equation is more suitable for simulating the propagation process of seismic waves in the overlying seawater elastic media. Through numerical simulations of a three-layered model, we have verified the feasibility of using towed streamer data for S-wave velocity inversion. Subsequently, we derived the waveform inversion gradient operator applicable to the acoustic-elastic coupled equation and established a method for P- and S-wave velocity waveform inversion of complex salt based on towed streamer data. Finally, we validated the applicability and accuracy of this new method through inversion tests conducted on a complex salt media model constructed based on actual overseas geological conditions, as well as through inversion trials using towed streamer data.