The magnetorheological fluid (MRF) semi-active suspension (SAS) is a crucial system for the absorption and the dissipation of vibration energy. However, the hysteresis nonlinearity of the MRF actuator is difficult to tackle in the control design of the MRF-SAS system. A novel robust finite frequency control strategy based on a Taylor approximation is proposed in this work to improve the vibration suppression of the MRF-SAS system with hysteresis nonlinearity. First, a hyperbolic tangent model is introduced to represent the nonlinear dynamic characteristics of the MRF damper, and then the modified Taylor expansion is adopted to approximate the hyperbolic tangent model. Moreover, an online sequential extreme learning machine (ELM) is employed to construct the inverse model of the MRF damper. Finally, to trade off vehicle handling stability and ride comfort, the robust finite frequency controller is designed based on the linear matrix inequations (LMIs) with the consideration of the time delay, the control perturbation, and the actuator saturation. It can be seen from the simulation results that the proposed robust finite frequency controller is more effective in improving vibration suppression of the MRF-SAS system than the skyhook controller.