In order to realize the safety protection of floating cultural relics during earthquakes, a nonlinear quasi-zero stiffness isolation system is analyzed. The stiffness model and the motion balance equation of the isolation system were established, and the harmonic balance method and Newton iterative method were used for theoretical analysis, and the fourth-order R-K method was used for numerical analysis of the motion balance equation under harmonic excitation and ground motion excitation. The theoretical analysis results show that the nonlinear quasi zero stiffness of cultural relics of the isolation system under harmonic excitation, outer excitation frequency is low frequency phase, the response of the system is unstable region, therefore, if the rigidity and damping ratio of the system is improved the unstable area and peak amplitude response of the system will be reduced, and make it tend to be characteristic of the linear vibration isolation system. Increasing the damping ratio can reduce the effective initial frequency of the isolation system, but increasing the damping ratio in the effective frequency band will increase the transfer coefficient of the system. Increasing the spring stiffness will increase the effective initial frequency of the isolation system, but reduce the amplitude response of the system in the low frequency stage, but increase the transfer coefficient of the system in the effective frequency band of the isolation system. Numerical analysis shows that there are only two stable solutions in the unstable region, and the response state of the system is related to the initial state of the system. The system can significantly reduce the acceleration response of input ground motion under the action of actual ground motion excitation. The damping coefficient of the isolation system is insensitive to the change of the input peak value of the ground motion with less long period components, but is sensitive to the change of the input peak value of the ground motion with more long period components, indicating that the isolation performance of the system is better for the short period ground motion, which is consistent with the theoretical analysis results under the action of simple harmonic excitation.