In the problem of inaccurate mathematical models of inerter-rubber vibration isolators， a nonlinear mathematical model based on the force-displacement relationship is established considering the restoring force of the isolators. Based on the mechanical property test， the Bouc-Wen model is used to simulate the hysteresis characteristics of the inerter-rubber vibration isolator ， and the genetic algorithm is used to identify the unknown parameters in the mathematical model. Moreover， the test data of different amplitudes and frequencies are used to check the results. Finally the Simulink toolbox is used to verify the numerical simulation results . The results show that the genetic algorithm can correctly identify the unknown parameters in the model. When the excitation frequency is 0.1 ~ 5 Hz， the maximum deviations of the upper and lower amplitudes of the test value and the simulated value are 7.9% and 8.3%， respectively. In the 10 Hz frequency band， the average error between the transmission rate obtained by the model and the experimental transmission rate is 8%， which is in good agreement with the test data， which verifies the correctness of the Bouc-Wen model of the inerter-rubber vibration isolator.