Aiming at the nonlinear characteristics of the vibration isolation system for naval equipments，a mathematical model of the nonlinear vibration isolation system including nonlinear stiffness，Coulomb damping and geometric nonlinear viscous damping is established，and the average method is used for analytical solution，the system stability boundary conditions are obtained according to the Routh-Hurwitz criterion. The influence of linear damping，Coulomb damping and geometrically nonlinear viscous damping on the system's amplitude-frequency response and stability is comprehensively studied. The jump avoidance parameter design of the nonlinear vibration isolation system is carried out，and the influence of the system parameters on the jump avoidance boundary is analyzed. It is verified by vibration test. The results show that linear damping，Coulomb damping and geometrically nonlinear viscous damping have positive effects on reducing the amplitude-frequency response peaks and improving system stability of soft and hard vibration isolation systems. Due to the "locking" characteristic of Coulomb damping，the amplitude-frequency response of the hard vibration isolation system appears "frequency island"，and the system stability cannot be effectively improved. However，Coulomb damping effectively reduces the amplitude-frequency response peak of the soft vibration isolation system and improves system stability；Geometrically nonlinear viscous damping has a significant effect on reducing the peak amplitude and frequency response and improving the stability of the system without the phenomenon of "frequency island". The design of the jump avoidance parameters of the nonlinear vibration isolation system and the obtained change rule of the jump avoidance parameters have an important guiding role in the parameter design of the nonlinear vibration isolation system.