Understanding the impact of dynamic effects induced by wave-current conditions on the hydrodynamic performance of a floating horizontal axis tidal turbine (HATT) is crucial toward developing floating tidal turbines to harness tidal energy in deep water sites. The complicated of the wake of a HATT has not yet been fully understood. In this paper, a Computational Fluid Dynamics (CFD) model used to study the performance of a turbine supported by a moored floating platform, due to surge only and in wave-current flows. The CFD model is compared against piled turbine tests, providing an error of 1.36% in power coefficients at the studied TSR = 3.9. It was shown that surge motion caused by even a small wave height or wavelength has a significant effect on the thrust and torque of the rotor. The wave height and period have a remarkable effect on the fluctuation of the hydrodynamic performance due to the induced rotor velocity. The surge motion affects the wake velocity recovery and vortex structure development. For a fuller understanding, future work could explore the negative effects such as induced blade fatigue and platform instability arising from surge motion, as to design cost-efficient turbines, supports and arrangements.