Installing vibration isolation devices on equipment is one of the important methods to ensure its stable use. From the perspective of bionics, according to the excellent impact resistance of cats when landing, this paper designs a high static and low dynamic stiffness isolator with asymmetric stiffness characteristics by observing their landing action posture and using the principle of nonlinear compensation and using the air spring as the positive stiffness structure. Taking it as the research object, a dynamic model is established, and a specific method is used to analyze and solve the asymmetric stiffness system, and compare it with the numerical results and finite element simulation results. The results show that at lower damping and higher excitation amplitudes, there is also a period response or even a chaotic response. At the same time, by comparing the vibration isolation structure and the vibration isolation performance of a single air spring designed in this paper, the conclusion that the vibration isolation effect is significantly better than that of a single air spring can be obtained, which verifies the effectiveness and feasibility of the designed vibration isolation structure.