In this paper a new model is developed to describe the response of Magneto-rheological fluids (MRF) in transient state. The models which are developed so far, cover the steady-state flow, or address the transient state, with step-wise input electrical current and constant shear rate. In this paper, a new model for transient state of MRF is developed in which the input electrical current is an exponential function in different values of shear rate. Due to the magnetic inertia caused by the inductance of the coil, the real magnetic flux density could not be step-wise. Hence, compare with the other models, this model is in well agreement with reality. To verify the presented model and study the fluid properties as input parameters, an experimental coupling is designed and fabricated. The coupling applies magnetic field perpendicular to shear direction, and measures the shear stress as a function of time. The results of the proposed model show acceptable agreement with experimental observations. According to experimental and theoretical results, the presented model is applied to a controllable torque coupling and acceptable results were obtained.