Magnetorheological (MR) damper is a promising semi-active device for vibration control of structures. This paper presents a simple mathematical model of MR damper with a small number of model parameters, which can express its hysteresis behavior of nonlinear dynamic friction mechanism of the MR fluid. The adaptive identification algorithm is also proposed in which the uncertain model parameters and internal state variable can be estimated in an online manner. The proposed model has an advantage that by using its inverse model we can analytically determine the necessary input voltage to the MR damper so that the desirable damper force can be added to the structure in an adaptive manner. Experimental results validate the proposed adaptive modeling method and the model-based inverse control approach in vibration isolation of three story structure.