The paper presents a study on the direct voltage control of a magnetorheological (MR) damper for application in vehicle suspensions. As MR damper dynamics is highly nonlinear, the direct control system design for an MR damper is difficult. Representing an MR damper by a Takagi–Sugeno (TS) fuzzy model enables the linear control theory to be directly applied to design the MR damper controller. In this paper, first the MR damper dynamics is represented by a TS fuzzy model, and then an H∞ controller that considers the suspension performance requirements and the constraint on the input voltage for the MR damper is designed. Furthermore, considering the case that not all the state variables are measurable in practice, the design of an H∞ observer with immeasurable premise variables and the design of a robust controller are proposed, respectively. Numerical simulations are used to validate the effectiveness of the proposed approaches.