In this paper, a new type of damping device NiTiNOL-steel wire ropes (NiTi-ST) are proposed. It is a vibration absorber with linear hysteresis damping and nonlinear damping. In this study, the NiTi-ST damping device is coupled with a functionally graded material (FGM) beam model. The Runge-Kutta method and the harmonic balance method are used to study the resonance response of the system from both numerical and analytical aspects. It is verified that NiTi-ST provides an effective vibration reduction effect for FGM beam. Changing the external environment temperature and humidity will affect the stiffness of the beam model, thus affecting the resonance peak value, but will not affect the damping effect of NiTi-ST. The simulation results confirm that NiTi-ST is a promising nonlinear damper and can be used as a new method for vibration suppression of continuous structures.