The floating horizontal-axis tidal current turbine (HATCT) moves with the floating carrier while rotating, resulting in a change in its relative inflow velocity at any time. If the rotating speed of the HATCT is fixed, the HATCT cannot work at the optimum tip speed ratio, resulting in the failure to achieve the optimum power generation efficiency. Therefore, this paper proposes a control strategy for the rotating speed of the HATCT, and obtains the hydrodynamic loads of the HATCT with variable speed rotation and pitching motion under free surface conditions based on the CFD method. Compared with the hydrodynamic load of the HATCT under the same situation but with fixed speed control, the variable speed control can effectively improve the power coefficient of the HATCT, but the load fluctuation in terms of the inflow direction load, power, and pitch moment coefficients are more significant than those with fixed speed control. On this basis, according to the variation law of the damping coefficient with pitch period, pitch amplitude, and tip speed ratio, the hydrodynamic load prediction method of the HATCT with pitching motion is established. The validity of this prediction method is verified by comparing the results with those of CFD calculation.