In this article, we present a methodology that leads to seismic vibration suppression of a class of base isolated civil structures by means of magnetorheological dampers. Magnetorheological dampers are versatile devices that generate damping force by controlling the rheological properties of the constituting magnetorheological fluid through a varying magnetic field. Magnetorheological dampers are more efficient than other devices in terms of energy requirements, damping force and mechanical design. However, they exhibit a complex behaviour, characterised by the hysteretic response to a velocity input, which is rather difficult to model. This in turn makes imperative the use of non-linear control techniques to achieve the final objective. In this article, Bouc?Wen model is used to describe the dynamics of an magnetorheological damper and adaptive backstepping controller is developed to explore its performance in seismic vibration suppression.