Vortex-induced vibration (VIV) of marine risers poses a significant challenge as the offshore oil and gas industry moves into deep water. A time-domain analysis tool has been developed to predict the VIV of marine risers based on a forcing algorithm and by making full use of the available high Reynolds number experimental data. In the formulation, the hydrodynamic damping is not treated as a special case but simply an extension of the experimentally derived lift curves. The forcing algorithm was integrated into a mooring analysis program based on the global coordinate-based finite element method. At each time step, the added mass, lifting force, and drag force coefficients and their corresponding loads are computed for each element. Validation studies have been carried out for a full-scale rigid riser segment and a model-scale flexible riser. The numerical results were compared with experimental data and solutions by other programs.