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This paper presents a mathematical modeling of a magneto-rheological (MR) brake to determine a relationship between input current and output torque for applying a variety of control applications. The proposed model is consisted of two sub-models: a mechanical sub-model, using Bingham plastic model for MR fluid and a magnetic circuit sub-model through a semi-empirical method to estimate the nonlinear hysteresis behavior of MR brake used. The first mechanical sub-model using Bingham plastic model describes the magnetic filed dependent fluid characteristics and the relationship between the torque and the dynamic yield stress caused by the applied field. The magnetic circuit makes up the second sub-model with the relationship between the dynamic yield stress and the magnetic induction of MR fluid. Due to the ferromagnetic property of the material used to form the flux path, MR brake experienced hysteresis effects and thus its hysteresis behavior is approximated through a semi-empirical method. The final model of MR brake links both sub-models together by the torque. An experimental setup is manufactured to evaluate the proposed model with a commercial MR brake used. The experimental result is compared with these predicted from the proposed nonlinear model in order to validate the model accuracy. The result shows that proposed model is reasonably predicted the hysteresis behaviors of MR brake. Moreover, the frequency response test of MR brake is carried out to evaluate the feasibility for a torque estimator in control use, and shows that the predicted frequency response matches up to the experimental characteristics and MR brake used has a bandwidth of nearly 35 Hz enough high to control.