Marine current turbines are submerged structures and subjected to loading conditions from both the currents and wave effects. The associated phenomena posed significant challenge to the analyses of the loading response of the rotor blades and practical limitations in terms of device location and operational envelopes. The effect of waves on marine current turbines can contribute to the change of flow field and pressure field around the rotor and hence changes the fluid forces on the rotor. However, the effect of the waves on the rotor depends on the magnitude and direction of flow velocity that is induced by the waves. An analysis is presented for predicting the torque, thrust, and bending moments resulting from the wave-current interactions at the root of rotor blades in a horizontal axis marine current turbine using the blade element-momentum (BEM) theory combined with linear wave theory. Parametric studies are carried out to better understand the influence of important parameters, which include wave height, wave frequency, and tip-speed ratio on the performance of the rotor. The periodic loading on the blade due to the steady spatial variation of current speeds over the rotor swept area is determined by a limited number of parameters, including Reynolds number, lift and drag coefficients, thrust and torque coefficients, and power coefficient. The results established that the BEM theory combined with linear wave theory can be used to analyze the wave-current interactions in full-scale marine current turbine. The power and thrust coefficients can be analyzed effectively using the numerical BEM theory in conjunction with corrections to the tip loss coefficient and 3D effects. It has been found both thrust and torque increase as the current speed increases, and in longer waves the torque is relatively sensitive to the variation of wave height. Both in-plane and out-of-plane bending moments fluctuate significantly and can be predicted by linear wave theory with blade element-momentum theory.