This paper proposes a novel design method for a magnetorheological (MR) damper-based semi-active suspension system. An improved MR damper model that accurately describes the hysteretic nature and effect of the applied current is presented. Given the unfeasibility of installing sensors for all vehicle states, an MR damper current controller that only considers the suspension deflection and deflection rate is proposed. A linear matrix inequality problem is formulated to design the current controller, with the objective of enhancing ride safety and comfort while guaranteeing vehicle stability and robustness against any road disturbance. A series of experiments demonstrates the enhanced performance of the proposed MR damper model, which exhibits greater accuracy than other state-of-the-art damper models, such as Bingham or bi-viscous. An evaluation of the vehicle behavior under two simulated road scenarios has been conducted to demonstrate the performance of the proposed output feedback MR damper-based semi-active suspension system.