Abstract: Isotropic magnetorheological elastomers (MREs) are smart materials fabricated by embedding magnetizable particles randomly into a polymer matrix. Under a magnetic field, its modulus changes rapidly, reversibly, and continuously, offering wide application potential in the vibration control area. Experimental observations show that there is a strong frequency, strain amplitude, and magnetic dependence of the dynamic behavior of isotropic MRE. Although important for potential applications, the magnetic-dependent nonlinear dynamic behavior of isotropic MRE has received little theoretical attention. To accurately evaluate the dynamic performance of isotropic MRE and to guide the design of isotropic MRE-based products, a new constitutive model based on continuum mechanics theory is developed to depict the magnetic-dependent nonlinear dynamic behavior of isotropic MRE. Subsequently, the numerical implementation algorithm is developed, and the prediction ability of the model is examined. The model provides a deeper understanding of the underlying mechanics of the magnetic-dependent nonlinear viscoelastic behavior of isotropic MRE. Furthermore, the model can be utilized to predict the magnetomechanical coupling behavior of isotropic MRE and therefore serves as a useful platform to promote the design and application of isotropic MRE-based devices.