Different　from　previous　researches　which　mostly　focused　on　linear　response　control　of　seismically　excited　high-rise　buildings,　this　study　aims　to　control　nonlinear　seismic　response　of　high-rise　buildings.　To　this　end,　a　semi-active　control　strategy,　in　which　H　infinity　control　algorithm　is　used　and　magneto-rheological　dampers　are　employed　for　an　actuator,　is　presented　to　suppress　the　nonlinear　vibration.　In　this　strategy,　a　modified　Kalman-Bucy　observer　which　is　suitable　for　the　proposed　semi-active　strategy　is　developed　to　obtain　the　state　vector　from　the　measured　semi-active　control　force　and　acceleration　feedback,　taking　into　account　of　the　effects　of　nonlinearity,　disturbance　and　uncertainty　of　controlled　system　parameters　by　the　observed　nonlinear　accelerations.　Then,　the　proposed　semi-active　H　infinity　control　strategy　is　applied　to　the　ASCE　20-story　benchmark　building　when　subjected　to　earthquake　excitation　and　compared　with　the　other　control　approaches　by　some　control　criteria.　It　is　indicated　that　the　proposed　semi-active　H　infinity　control　strategy　provides　much　better　control　performances　by　comparison　with　the　semi-active　MPC　and　Clipped-LQG　control　approaches,　and　can　reduce　nonlinear　seismic　response　and　minimize　the　damage　in　the　buildings.　Besides,　it　enhances　the　reliability　of　the　control　performance　when　compared　with　the　active　control　strategy.　Thus,　the　proposed　semi-active　H　infinity　control　strategy　is　suitable　for　suppressing　the　nonlinear　vibration　of　high-rise　buildings.