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In this study, the motions of a moored buoy and its surrounding fluid flow are numerically studied. The solver is developed by coupling the computational fluid dynamics platform, OpenFOAM, with a lumped mass mooring line model, MoorDyn. The time marching interface to transfer the solution variables is developed for the robustness and accuracy of the solver. The developed coupled solver was validated against a moored cubic-shaped box model in waves. The different mesh configurations, mesh generation technique and mooring line discretization are considered in the numerical study. A cubic-shaped box attached with tensioned mooring lines in waves is simulated and the results are compared with the experimental results. Motion responses of a moored semi-submersible platform, which is designed by Korea Research Institute of Ship and Ocean Engineering (KRISO), in waves are predicted by the solver. The mooring line tensions acting on the body and anchor, the forces acting on the platform and the platform's motion performance are analyzed, and comparisons are made between simulation data and experimental data.