Abstract The control of the stationary response of a half car vehicle model moving with a constant velocity over a rough road with magnetorheological (MR) dampers is considered. The MR damper is modelled by the modified Bouc–Wen model. The MR damper parameters adopted in the vehicle model correspond to an actual fabricated damper and are determined so that the MR damper model characteristics match with experimental characteristics. The random road excitation is considered as the output of a first-order linear shaping filter to white noise excitation. The control and response statistics of the nonlinear vehicle model with MR damper are obtained using the equivalent linearization method in an iterative manner and the results are verified by Monte-Carlo simulation. The MR damper performance is sought to be improved by suitable choice of input currents to the levels of performance of an active suspension based on H ∞ control without and with preview by a mean square equivalence of respective control forces. The H ∞ optimal control with preview minimizes a performance index which is a weighted sum of vehicle performance measures such as sprung mass acceleration, pitch acceleration, front and rear suspension strokes, road holding and control forces with the weights obtained by solving a multi-objective optimization problem using a non-dominated sorting genetic algorithm II (NSGA II).