To improve knowledge of the unsteady hydrodynamic characteristics of a floating horizontal-axis tidal turbine (HATT) in complex marine environments, a computational fluid dynamics (CFD) numerical method is established to analyze the functioning of a HATT under free surface and pitch conditions: an amplitude of 2.5°–12.5° and a period of 3–15 s. The appropriateness of the CFD method is validated against piled turbine tests in a circulating flume, which turned out to be only 1.43% off at the rated tip speed ratio. The power and thrust coefficients exhibit periodic variation with a frequency twice the pitch's motion. From the ecological perspective, the wake velocity field presents radial warps accompanied by several ellipsoidal low-velocity core regions, which corresponds to the fused vortex rings in the vortex zone. Notably, the wake is more influenced with large rather than small amplitudes and periods; meanwhile, the wake is more sensitive to frequency changes than to amplitude changes. The results could lay a foundation for future research into more complex motion response of floating tidal turbines.