In order to study the energy absorption characteristics and dynamic response rule of constant resistance and large deformation with negative Poisson’s ratio (NPR) anchor cable under the action of earthquake, the physical model test on the tunnel passing through a fault supported by common anchor cable and NPR anchor cable was carried out by using the shaking table test. The dynamic response rule of tunnel structure under different surrounding rock conditions and supported by different anchor cables under the action of earthquake was compared and analyzed. The results show that the damage degree of tunnel structure supported by NPR cable is significantly improved compared with that supported by common cable under the same seismic wave. This suggests that NPR cable has good energy absorption characteristics and can provide effective support for tunnel structure under earthquake. By comparing and analyzing the time-history curves of axial force of common cable and NPR cable, it is evident that under the action of seismic waves, the common cable will break and the axial force will drop to zero, while the high constant resistance of NPR cable can continue to provide effective support. By analyzing the dynamic response of acceleration, strain and earth pressure at each measuring point of the tunnel structure, it can be seen that the dynamic response of the tunnel fault area is more obvious, and the tunnel structure fails in the sequence of arch spandrel→haunch→crown under the action of earthquake. This research achievement provides a theoretical reference for support strategies in tunnel engineering.