Abstract: A new type of isolator with multi-types of damping and nonlinear stiffness through oil,air,rubber and spring coupling by ingenious tactics is presented in references.In this paper,a mathematical model of a multi-medium coupling isolator is developed for attenuating wide-band random vibration for practical applications.The model considers the coupling of quadratic damping,viscosity damping,coulomb damping and nonlinear spring.The approximate theoretical calculating formulae are deduced by combining FPK transform and equivalent principle method.By conducting parametric analysis,it is shown that changes in the nonlinear characteristic parameters would induce changes in the system characteristics.The solution establishes a theoretical basis for further research.