The hydrodynamic performance of a turbine with multi-degree of freedom (rotation, rolling, surging) coupled motion in the unbounded uniform flow is analysed by the sliding and dynamic meshes. The effects of the turbine's hydrodynamic load has been studied and illustrated considering the coupled motion of rotation, rolling and surging. Numerical results shows that: 1) the effects of the hydrodynamic load is mainly caused by the surging motion, namely, the instantaneous values of the axial load and power coefficients generate fluctuation with a frequency that is the same as that of the surging and an amplitude that similarly increases in parallel. The effect of the rolling motion on hydrodynamic load will be reflected when its frequency is greater than that of the surging; 2) the calculation formulas of the turbine's axial load and power coefficients has been obtained. The results of the hydrodynamic load calculated by the calculation formula and CFD numerical simulation show good agreements, which verify the calculation formulas. The results of this research can provide relevant data for the hydrodynamic analysis of turbines with multi-degree of freedom motion and verify the structural design and control of the electric output.