It　is　effective　to　install　MR　damper　on　an　adjacent　structure　to　mitigate　its　seismic　responses　and　prevent　pounding　during　earthquake.　Here,　trust-region-based　instantaneous　optimal　semi-active　control　algorithm　(TIOC)　was　induced　to　an　adjacent　structure　with　MR　damper　installed　under　earthquake　excitations.　Based　on　its　equations　of　motion,　the　optimized　equations　of　the　semi-active　control　problem　were　built.　And　then　the　TIOC　optimization　problem　subjected　to　a　bound　constraint　was　deduced,　and　the　optimal　semi-active　control　forces　were　calculated　at　every　time　step.　Finally,　simulation　was　conducted　for　an　adjacent　structure　with　MR　dampers　installed　using　TIOC　algorithm.　The　results　showed　that　the　seismic　responses　of　the　adjacent　structure　can　be　reduced　effectively;　compared　with　Clipped-optimal　control　algorithm,　TIOC　algorithm　is　more　capable　of　controlling　the　relative　displacement　between　structures　close　to　each　other;　TIOC　algorithm　has　better　adaptability;　the　controller＇s　behavior　can　be　significantly　changed　with　the　objective　function　and　thus　it　should　be　selected　carefully.