Abstract: A mechanical vibration system with a novel 2DOF nonlinear energy sink (NES) is studied. The nonlinear energy sink structure is constructed and the motion equation of the whole system is established. The nonlinear force acting on the second-order oscillator is approximately expressed by Taylor series and the numerical method is used to analyze the vibration reduction performance of the NES. The conditions of the targeted energy transfer in the NES are studied in terms of its structural parameters and the initial energy. It is shown that the NES can effectively reduce the energy of the main structure and the vibration suppression effect of the NES is better than that of the single degree of freedom NES.