Relying on the ultra-stable vehicle-mounted vibration isolation platform， a quasi-zero stiffness system composed of wrap-around lateral elastic supports is established， and the nonlinear dynamic characteristics of the system and the active vibration adjustment method are studied to obtain excellent vibration isolation effect. The structural parameters of the system are determined according to the relationship between the overall stiffness and displacement of the system， and the harmonic balance method is used to obtain the dynamic response law and nonlinear amplitude-frequency response function of the system. The nonlinear bifurcation characteristics of the system are further studied on the active control method， the bifurcation control method of the quasi-zero stiffness system is obtained， and the bifurcation of the system is eliminated by selecting appropriate control parameters. The simulation results show that the bifurcation control method can effectively eliminate the bifurcation and achieve the effect of vibration suppression under the appropriate control parameters.