For the fast prediction of the hydrodynamic characteristics of a floating horizontal-axis tidal current turbine (HATT) with coupled rotation and surging motion, this study applies the CFD method to simulate the coupled rotation and surging motion, and obtains the axial force and axial torque coefficients at different current velocities. According to the CFD simulation data, the constant force, damping, and added mass coefficients can be obtained by least-squares fitting. The approximate calculation formulas of the axial force and axial torque coefficients of a turbine with coupled rotation and surging motion are summarized by analyzing the constant force, damping, and added mass coefficients under different surge frequencies and amplitudes, turbine rotation speeds, and current velocities. The results demonstrate the following: 1) the frequency and amplitude of the surge have little impact on the damping coefficient, which is positively proportional to the tip speed ratio; 2) when predicting the hydrodynamic load of a turbine with coupled rotation and surging motion, the added mass coefficient can be neglected, and only the influence of the constant terms of the constant force and the damping coefficients are needed. The approximate calculation formula obtained in this study can effectively predict the hydrodynamic load of the HATT.