The vibration suppression of structures using a semi-active mass damper is investigated in this study. A magnetorheological (MR)-damper is utilized to design the semi-actively controlled mass damper. The inverse MR-damper model is developed on the basis of an improved LuGre friction model, and combined with a designed /Linear-Quadratic-Gaussian (/LQG) controller, in order to control the command current of the MR-damper to suppress structural vibration levels effectively. Illustrated examples are considered to investigate the vibration suppression effectiveness of a semi-active mass damper with a MR-damper, using the developed control methodology. The simulation results were compared with those reported in literature in order to validate the presented methodology.