A new 3D Terbium (III) metal-organic framework has been solvothermally synthesized by using terbium ion as the metal center and 1,1'',1''''-(2,4,6-trimethylphenyl-1,3,5-tri) trimethyl tritrium (4-carboxylpyridyl) tribromide (H3LBr3) as ligand. The molecular formula is [Tb(H3LBr3) (OH)(2)](NO3)(DMAC)(3). Compound crystallizes in the triclinic system, space group P-1-1, with a=9.5747(8)=9.5747(8), b=12.8667(10)=12.8667(10), c=18.9440(14)=18.9440(14)angstrom, alpha=107.619(2)degrees=107.619(2)degrees, beta=99.057(2)degrees=99.057(2)degrees, gamma=97.615(3)degrees=97.615(3)degrees, V=2156.0(3)=2156.0(3)angstrom(3), Z=2=2, Mr=1041.85=1041.85, Dc=1.605=1.605g/cm(3), mu=1.717=1.717mm-1-1, F(000)=1068(000)=1068, R=0.0583=0.0583 and wR=0.1262=0.1262 for 7586 observed reflections (I>2 sigma>2 (I)). Meanwhile, the fluorescence property was also studied. The result shows that the synthesized Tb-MOF displays highly selective sensing of acetone.