Wave induced motions due to actual sea state conditions will impact the performance of floating counter-rotating type tidal turbines. The wave-current interaction is a significant factor in determining the heave motion of turbines. The present study aims at investigating the effects of heave motion on the performance of a floating counter-rotating turbine under wave-current interaction. In this study, the numerical method is used to study how the heave amplitude and frequency affect the main hydrodynamic coefficients of the turbine, including the power coefficient and thrust coefficient. The form of sliding mesh combined with overset mesh is adopted, and the heave motion of the turbine is realized by the movement of the overset mesh. The simulation results show that the heave motion has an adverse effect on the hydrodynamic performance of the counter-rotating tidal turbine. The heave motion will reduce the mean power coefficient and the mean thrust coefficient by about 9% and 5% respectively. The reduction in mean thrust and power is mainly due to less optimal rotor operation caused by the hydrodynamic effects associated with oscillating inflow. The front propeller is more susceptible to heave motion than the rear propeller. Furthermore, the effects of wave on the hydrodynamic performance of turbine are studied by changing the immersion depth of the turbine. The wave will increase the power coefficient slightly, but at the same time, also increase the probability of heave motion. The results can provide data to study motion response of floating tidal turbines under wave-current interaction and control design of the output electricity.