A circular wire-cable vibration isolator is designed by adopting independent wire rope loops as elastic damping elements. Owing to its unique structure, the isolator exhibits nonlinear elastic stiffness and asymmetric hysteresis dynamic behavior in the tension–compression mode. In the present study, a modified normalized Bouc-Wen model is proposed to describe the hysteretic behaviour of a circular wire-cable vibration isolator. A two-stage identification method is developed for identifying the model parameters. Periodic loading experiments were carried out to validate the proposed model and identification method. The results verify that the proposed model and identification method are effective for accurate description of asymmetric hysteresis dynamic behavior in the tension–compression mode of circular wire-cable vibration isolator. It establishes the foundation for dynamic design method of circular wire-cable vibration isolator.