A better understanding of the phenomenon of wave-seabed-structure interactions is essential for the evaluation of the liquefaction of seabed foundation under dynamic loading in the ocean environments. However, only a few investigations have been conducted for the cross-anisotropic seabed under wave pressure and marine structures, despite the fact that most seabeds are anisotropic medium. Furthermore, most previous numerical models for Biot's consolidation theory were only considered wave loading. In this study, based on Biot's partly dynamic poroelastic theory ("u-p" approximation), a two-dimensional FEM seabed model is adopted to investigate the wave and current induced seabed response around a submarine pipeline. The third-order solution of wave-current interactions is used to determine the dynamic pressure acting on the seabed. Verification of the proposed model is performed against the previous experimental data and analytical result. With the proposed numerical model, the effects of wave, current and seabed characteristics, such as Poisson's ratio, Young's modulus, degree of saturation, and pipeline buried depth on the wave-induced seabed response will be examined. Then, the wave-current induced seabed liquefaction is also discussed. The numerical results demonstrate significant effects of anisotropic soil behavior on seabed liquefaction.