It is known that surface waves have significant influence on the hydrodynamic performance of ocean current turbines which locate near the water surface. In order to quantitatively analyze the wave influence and reveal the interaction mechanism between the wave and the turbine flow, this paper proposes a three-dimensional transient computational fluid dynamics (CFD) model which can accurately predict the hydrodynamic performance of ocean current turbines under current-wave interaction flow conditions. The influences of two key wave parameters, the wave height and the submerged depth of the turbine, on the hydrodynamic forces and flow structures of a three-bladed horizontal axis ocean current turbine are discussed in depth. It is found that the both the average value and the oscillation amplitude of the torque on the turbine increase with the increased wave height, but decrease with the increase of the submerged depth. It is also found that in the cases of shallow submerged depth, the wake structures of the turbine are affected by the surface wave.