In this paper, Simple Adaptive Control (SAC) method is used to mitigate the detrimental effects of earthquakes on MR-damper equipped structures. Acceleration Feedback (AF) is utilized since measuring the acceleration response of structures is known to be reliable and inexpensive. The SAC is simple, fast and as an adaptive control scheme, is immune against the effects of plant and environmental uncertainties. In the present study, in order to translate the desired control force into an applicable MR damper command voltage, a neural network inverse model is trained, validated and used through the simulations. The effectiveness of the proposed AF-based SAC control system is compared with optimal H2/LQG controllers through numerical investigation of a three-story model building. The results indicate that the SAC controller is substantially effective and reliable in both undamaged and damaged structural states, specifically in reducing acceleration responses of seismically excited buildings.