To suppress the torsional vibration of the rotor system, a rubber-based nonlinear energy sink (RNES) is developed. The action mechanism of RNES is the piecewise linear stiffness produced by extrusion of the rubber blocks. The structure of the RNES is designed, the dynamic model of the RNES-rotor system is built, and the ability to suppress the torsional vibration of the rotor system is evaluated by the transient torsional vibration and the steady-state torsional vibration. In transient vibration suppression, the percentage of accumulated energy dissipation of RNES can reach 93.3%. For steady-state vibration suppression, the peak vibration suppression of RNES can reach 83.2% in simulation and 78.6% in test. In addition, the broadband vibration alleviation performance of the RNES is simulated, and the vibration reduction ability of RNES and a linear dynamic vibration absorber (LDVA) with the same rotary inertia is compared.