With a wave-current generator designed in a numerical wave tank (NWT), we extended our highly efficient Navier-Stokes solver (Li et al., 2004a;b) for modelling of wave-current-structure interactions. This solver (named LVOF) is constructed by a novel VOF finite volume approach that incorporates surface tension, coupled with a dynamic subgrid-scale (SGS) turbulence model. The numerical generator located in the inflow boundary oscillates vertically the combined motions of waves and currents starting from its static stage, while the outgoing waves downstream are dissipated by a breaking-type absorber placed in the tank extremity (or a numerical damping zone). Test cases concern a combination of wave propagation, current, shoaling, reflection and breaking, when overtopping of waves over a seadike and seawall, including the study in the channel wave motions following and opposing a current. By using LVOF, our results demonstrate that most of typical features in the wave-induced motions can be captured in waves superimposed on the following (or opposing) currents. By comparison, the velocity profile and the wave train are in good agreement with measurements available.