Recently, magnetorheological elastomer (MRE) has been paid increasingly attention for vibration mitigation devices with the benefits of low power cost, fail safe performances, and fast responses. To make full use of the striking advantages of MRE device, a highly precise model should be developed to predict its dynamic performances. In the work, an MRE isolator in shear–squeeze mixed mode is developed and tested under dynamic loadings. The nonlinear performances in various displacement amplitude and currents are shown. An artificial neural network model with a back-propagation algorithm is proposed to characterize the nonlinear hysteresis of MRE isolator for its implementation in vibration control applications. This model utilized the displacement, velocity, and applied current as inputs and output force as output. The results show that the proposed model has high modeling accuracy and can well portray the complicated behaviors of MRE isolator with different excitations, which shows a fundamental basis for structural vibration control.