Three novel 3D metal-organic frameworks, {[Zn2(L)(BDC)2]•H2O}n (1), {[Cd2(L)2(BDC)]•(BDC)•7.7(H2O)}n (2), and {[Co(L)(H2O)2]•(BDC)•5(H2O)}n (3)(L = tetrakis(imidazol-1-ylmethyl)methane, H2BDC = 1,4-benzenedicarboxylic acid), have been successfully synthesized by self-assembly of transition-metal salts with a flexible N-containing ligand and 1,4-dicarboxybenzene ligand. Complexes 1-3 have 3D structures with various topologies. In complex 1, the L connects Zn(II) atoms to form 2D layers, which are linked by two kinds of 1D [Zn(BDC)]n chains to generate a 4-connected three-dimensional structure with (6•8 5)(6 4 •8 2)(8 6) topology. In complex 2, Cd(II) atoms are coordinated by L to furnish a 2D layer, and the adjacent layers are linked by BDC ligands as bridging ligands to general a new (4,5)-connected three-dimensional network with a point symbol of (4 4 •6 2)(4 4 •6 6). In Complex 3, the L ligands act as 4-connected linkers connecting Co(II) ions to display a 4-connected three-dimensional structure with 4•6 5 topological net directly. In addition, the solid-state fluorescence, infrared spectra, magnetic property and thermal stability of these complexes have also been investigated.