Tuned　mass　damper　(TMD)　can　reduce　the　dynamic　response　of　a　structure　under　earthquake,　but　the　traditional　TMD　is　not　effective　to　reduce　translation-torsion　coupled　vibration　of　a　structure.　Here,　a　two-directional　horizontal　and　torsional　TMD　including　tuned　mass　blocks,　torsional　mass　blocks　and　rotation　lever　was　proposed.　The　horizontal　and　torsional　vibration　responses　of　a　structure　were　controlled　by　means　of　the　translation　and　the　rotation　of　a　multi-dimensional　tuned　mass　damper　(MDTMD)　in　different　directions.　According　to　the　movement　mechanism　of　a　MDTMD,　the　equation　of　motion　for　the　control　system　considering　eccentric　torsion　effect　was　derived.　An　eccentric　structure　with　MDTMD　was　analyzed　to　verify　its　control　performance　for　the　horizontal　and　torsional　coupled　vibration　system　under　earthquake,　and　its　vibration　reduction　effect　was　compared　with　that　of　the　traditional　TMD.　The　results　showed　that　the　coupled　response　can　be　reduced　effectively　with　a　MDTMD　and　the　vibration　reduction　efficiency　is　much　higher　than　that　of　the　traditional　TMD.