The problem of vibration attenuation in a semiactive vehicle suspension is considered. The proposed solution is based on usage of the information about the road roughness coming from the sensor installed on the front axle of the vehicle. It does not need any preview sensor to measure the road roughness as other preview control strategies do. Here, the well-known Skyhook algorithm is used for control of the front magnetorheological (MR) damper. This algorithm is tuned to a quarter-car model of the front part of the vehicle. The rear MR damper is controlled by the FxLMS (Filtered-x LMS) taking advantage of the information about the motion of the front vehicle axle. The goal of this algorithm is to minimize pitch of the vehicle body. The strategy is applied for a fourdegree-of-freedom (4-DOF) vehicle model equipped with magnetorheological dampers which were described using the Bouc-Wen model. The suspension model was subjected to the road-induced excitation in the form of a series of bumps within the frequency range 1.0-10 Hz. Different solutions are compared based on the transmissibility function and simulation results show the usefulness of the proposed solution.