The frequency response model of the chiral structure with three ligaments is built using finite element method. By the unit harmonic excitation force, the displacement responses of the point of applying unit force and a point far away from that point are obtained. The effects of different geometric parameters and the filler in the nodes on the response characteristics under medium–low frequency are studied. The results indicate that the node radius, ligament thickness, and ligament length have significant effects on the frequency response characteristics of the chiral structure with three ligaments. The starting frequency and the gap width of the frequency gap can be adjusted by changing the node radius of the limited periodic chiral structure. The filler in the nodes can change the starting frequency and width of the frequency gap. Hence, the narrow band gap under low frequency is obtained. When the frequency of the vibration is in the band gap, the chiral structure with the three ligaments has good attenuation characteristics. The results of this paper can provide the references for the design of chiral structure in the aeronautic and aerospace engineering.