The deepwater catenary mooring line damping mainly includes hydrodynamic drag damping, internal damping and friction damping caused by seabed interaction. Hydrodynamic drag and friction damping is significantly affected by a floating platform besides the internal damping caused by material properties. The dissipated energy by a mooring line from the floating platform as a result of its oscillation is applied to calculate the mooring-induced damping. The mooring line and seabed interaction is based on the hypothesis of rigid seabed. The fluid drag force and inertia force on the mooring line are calculated according to the Morrison formula. Under the various current velocity distribution conditions, the non-liner dynamic analysis of mooring line is executed in the time-domain based on the finite element method. Moreover, the wave drift oscillation and the wave frequency oscillation excitation of floating platform are specified. The maximum tension of mooring line and the viscous damping are obtained from the results. Considering the contact friction between the mooring line and seabed, the maximum tension of mooring line is compared under various friction coefficients and the friction damping is calculated.