To better understand the physical processes involved in the wave–seabed–pipeline interactions (WSPI), a three-dimensional numerical model for the wave-induced soil response around an offshore pipeline is proposed in this paper. Seabed instability around an offshore pipeline is one of the key factors that need to be considered by coastal engineers in the design of offshore infrastructures. Most previous investigations into the problem of WSPI have only considered wave conditions and have not included currents, despite the co-existence of waves and currents in natural ocean environments. Unlike previous studies, currents are included in the present study for the numerical modeling of WSPI, using an integrated FVM model, in which the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equation is used to solve the mean fluid field, while Biot’s consolidation equation is used to describe the solid–pore fluid interaction in the porous medium. Numerical examples demonstrate a significant influence of ocean current direction and angle on the wave-induced pore pressures and the resultant seabed liquefaction around the pipeline, which cannot be observed in two-dimensional (2D) numerical simulation.