Nonlinear energy sink is a kind of vibration energy absorption device, which plays an important role in vibration suppression of structure. In this paper, the correlation analysis of vibration suppression for a system with combined nonlinear damping nonlinear energy sink is carried out. Firstly, the theoretical model of the system with combined nonlinear damping nonlinear energy sink is described. The motion equations of the system model are derived by using the complex variable average method, and the slow variable equations of the system are obtained. Secondly, the slow variable equations of the system are analyzed by using the multi-scale method. By studying the slow invariant manifold and phase trajectories of the system, the condition basis of the strongly modulated response of the system is described. In addition, the influence law of the external excitation amplitude on the frequency detuning coefficient interval in the presence of the strongly modulated response is revealed by analyzing the system with one-dimensional mapping. Finally, the energy spectrum, time response and Poincare mapping are applied to study the vibration suppression of the system with combined nonlinear damping nonlinear energy sink, the influence law of different damping ratio, damping and stiffness of nonlinear energy sink on its vibration suppression effect is revealed. Meanwhile, it is found that the response of the nonlinear energy sink with combined nonlinear damping is consistent with that of the main structure. In addition, it is verified that the nonlinear energy sink with combined nonlinear damping proposed in this study has good vibration suppression ability.