Precise and real-time nonlinear hysteresis model of magnetorheological (MR) dampers is the premise to efficient control of MR semi-active systems. The influence of hysteresis models of MR damper on the control performance of the systems, employing a quarter-car MR semi-active suspension as an example, is studied thoroughly in this paper. Specifically, the hysteretic mechanical behavior of MR damper is precisely described, and the real-time feedforward control force tracking of MR damper is conducted, based on the resistor-capacitor (RC) operator-based hysteresis model. In addition, the dynamic model of a quarter-car MR semi-active suspension system is established, and a linear quadratic regulator controller and a Skyhook controller are correspondingly designed. The experimental tests, comparison, and analysis of MR damper utilizing the RC operator-based hysteresis model and the Bingham hysteresis model are carried out with the self-developed prototype of the quarter-car suspension system.