Usually, mooring system restoring forces acting on floating offshore structures are obtained from a quasi-static mooring model alone or from a coupled analysis based on potential flow solvers that do not always consider nonlinear mooring-induced phenomena or fluid-structure interactions and the associated viscous damping effects. By assuming that only the mooring system influences the restoring force characteristics, the contribution of mooring-induced damping to total system damping is neglected. This paper presents a technique to predict hydrodynamic damping of moored structures based on coupling the dynamic mooring model with a Reynolds-averaged Navier-Stokes (RANS) equations solver. We obtained hydrodynamic damping coefficients using a least-square algorithm to fit the time trace of decay tests. We analyzed a moored offshore buoy and validated our predictions against experimental measurements. The mooring system consisted of three catenary chains. The analyzed response comprised the decaying oscillating buoy motions, the natural periods, and the associated linear and quadratic damping characteristics. Predicted motions, natural periods, and hydrodynamic damping generally well agreed to comparable experimental data.