During aircraft braking, the change of ground adhesion forces can cause forward and backward vibration of the landing gear, and the performance of the brake disc may exacerbate this vibration. In order to solve this problem, a rigid–flexible coupling dynamic model of a two-wheel strut landing gear considering the friction characters of brake discs with different materials and a hydraulic brake system model is established in this paper. The brake disc friction characteristics effect on the low-frequency brake-induced vibration of the landing gear given different brake disc materials and ambient temperatures is studied. It is shown that the C/SiC brake disc has a “negative slope” phenomenon between the friction coefficient of the brake disc and the wheel speed, and this variable friction characteristic has a great effect on the low-frequency braking-induced vibration of the landing gear. In addition, the variable friction characteristics of the C/SiC brake disc are easily affected by ambient temperature, while the friction coefficient of the C/C brake disc changes stably.