For a current turbine fixed on a floating platform, the wave-induced motion responses of the platform change the hydrodynamic performance of the current turbine. In this paper, a numerical simulation method based on commercial computational fluid dynamics software-CFX is established to systematically analyze the turbine loads condition and power output efficiency of the turbine subject to the wave-induced motion. This method works well in terms of 2D hydrodynamic performance analysis and is verified by an experiment. In addition, the method is applied to investigate the hydrodynamic performance of a vertical axis current turbine under forced oscillation by a combining sliding mesh with moving mesh technique. This research mainly focusses on the effects of oscillation frequency and oscillation amplitude on the hydrodynamic performance and the flow field. It is found that a wake flow similar to the Von Karman Vortex Street appears under sway oscillation. Spacing between vortex in the wake flow changes under surge oscillation. The fluctuations of the blade load coefficients can be decomposed into a low frequency part and a high frequency part. The low frequency part is related to the frequency of the forced oscillation, while the high frequency part is a consequence of the rotational frequency of the turbine. The oscillation amplitudes of the turbine load coefficients increase linearly with the growth of oscillation frequency and oscillation amplitude. This paper can provide a useful reference for similar research on the turbine loads condition and power out efficiency of the turbine subject to wave-induced motion. This paper can also provide a reference on the structural design or electronic control of vertical axis current turbines.