Traditional　tuned　mass　damper　(TMD)　can　reduce　the　dynamic　response　of　structure　under　earthquake,　but　the　traditional　tuned　mass　damper　is　not　effective　to　reduce　translation-torsion　coupled　vibration.　A　two-directional　horizontal　and　torsional　tuned　mass　damper,　which　includes　tuned　mass　blocks,　torsional　blocks　and　rotation　lever,　is　proposed.　The　horizontal　and　torsional　response　of　the　building　structure　is　controlled　by　the　movement　and　the　rotation　of　the　multi-dimensional　tuned　mass　damper　(MDTMD)　in　different　directions.　According　to　the　movement　mechanism　of　the　MDTMD,　the　dynamic　equation　for　the　control　system　considering　eccentric　torsion　effect　is　established.　An　eccentric　structure　with　MDTMD　is　analyzed　to　verify　the　control　effctive　for　the　horizontal　and　torsional　coupled　system　under　earthquake,　and　the　reduction　effect　is　compared　with　the　traditional　TMD.　The　results　show　that　the　coupled　response　can　be　reduced　effectively　by　MDTMD　and　the　vibration　reduction　ration　is　much　higher　than　traditional　TMD.　©　(2014)　Trans　Tech　Publications,　Switzerland.