To ensure the long-term reliability of tidal stream turbines, waves and currents must be considered during the design phase. In this paper, a three-bladed horizontal axis turbine with a diameter of 0.9 m was used as the baseline model. OpenFOAM, an open-source computational fluid dynamics (CFD) library platform, was used to predict the performance of a horizontal axis tidal stream turbine (HATST) under waves and currents. A mesh dependency test was carried out to select the optimal mesh to capture the flow’s features. As a validation study, the power of the turbine under only the current was predicted and was found to be consistent with the experimental results. The generated wave profile under a current was compared with the results obtained using the third-order Stokes wave theory. The performance of the HATST was predicted for various wave frequencies and heights and compared with experimental data. The effect of the wave height on the power performance was greater than the wave frequency. Vortical flow structures behind the turbine were investigated for various wave conditions. The generated tip vortices propagated upward and downward at wave crest and trough conditions, respectively.