In this paper, vibration suppression of deep-sea flexible tension legs based on nonlinear energy sink is studied. Considering a tension leg mechanical model with parametric excitation and nonlinear energy sink (NES), differential equation of motion for nonlinear vibration control is derived by using Hamiltonian variational principle, and the Galerkin method was used for discretization. The transverse displacement modal vibration response of the flexible tension leg is obtained by numerical simulation, and vibration damping performances of NES and TMD are compared. The results show that the nonlinear energy sink has a more significant damping effect. Vibration control can be improved by adjusting the parameters of NES absorber.