A three-dimensional numerical model is developed in this study to investigate the problem of wave-current-body interaction. The model solves the spatially averaged Navier-Stokes equations. Turbulence effects are modeled by a subgrid-scale (SGS) model using the concept of large eddy simulation (LES). The model is employed to study the wave-current interaction with a square cylinder that is mounted on the bottom and vertically pierces the free surface. The force analysis demonstrates that the presence of waves can reduce both the strength and frequency of vortex shedding induced by a uniform current due to the nonlinear wave-current interaction. The free surface elevation, strain rates of the mean flow, and eddy viscosity are found to closely correlate with the mechanism of vortex shedding. It is also shown that when the vortex shedding is neglected in the calculation such as by the potential flow approach, one may significantly underestimate the magnitude of in-line force. The energy spectral analysis reveals that there exist initiating, growing, and decaying regions for shedding vortices around the cylinder. In the vortex initiating region, both coherent and turbulent structures are nearly two-dimensional that become three-dimensional in the vortex growing region. The kinetic energy of both coherent and turbulent motions is dissipated in the vortex decaying region, within which the mean flow gradually returns back to two-dimensional.