Nonlinear energy sinks (NESs) are a type of passive mass dampers reducing structural responses of main bodies with their nonlinear restoring force. A new type of NES called track NES consisting of a specially shaped track fixed on a main body structure and an auxiliary mass moving along the track was proposed here. Nonlinear restoring force was produced by changing the shape of the track. Firstly, theoretical analysis was performed to derive the expression of track NES’s nonlinear restoring force and equations of motion for a structure with a track NES attached. Numerical optimization was then carried out for a 2-DOF main structure with a track NES attached. It was shown that the optimized track NES has a good vibration reduction performance, and better robustness against changes of the structural stiffness of the main structure; the performance of the track NES, however, is sensitive to input energy level. To improve its energy robustness, the damping of the track NES was further investigated. The results showed that when the stiffness of the structure and the initial velocity are constant, the damping of the track NES can be optimized to make the structure vibration attenuation effect optimal, i.e., adjusting its damping can improve the track NES’s energy robustness.