A series of dynamic tests was carried out on an O type wire-cable vibration isolator by imposing cyclic sinusoidal motion to obtain its variations in hysteretic behavior with excitation amplitude and frequency in shear, roll and tension-compression, respectively. In shear and roll modes, the isolator exhibited symmetric hysteresis loops under cyclic loading. In the tension-compression mode, the isolator exhibited asymmetric hysteresis loops. As the displacement amplitude increased, stiffening and softening occurred along the tension and compression direction, respectively. The hysteresis loop area increased, and the asymmetric hysteresis became apparent. The rate-independent nature of wire cable isolators in the tested frequency range has been experimentally verified in shear, roll and tension-compression. A modified normalized Bouc-Wen model and a simple yet effective identification method were proposed to describe the hysteretic behavior of the isolator in three modes. The proposed model and identification method were validated with the results, which verified that the predicted hysteresis loops were close to the measured hysteresis loops, and the proposed model and method were effective for describing dynamic hysteresis behavior of vibration isolator in three modes.