A series of six coordination polymers, namely, [Cd-1.5(L)] (1), {Cd-1.5(L)(bpp)] (2), {{Cd-1.5(L)(p-bix)]center dot H2O}(n) (3), {Cd-1.5(L)(m-bix)(n) (4), {{Cd-1.5(L)(dpa)(3)(H2O)center dot 2H(2)O}(n) (5), and {{Cd-1.5(L)(bpbd)(2.5)]center dot 2H(2)O} (6) (Na3L = (S)-(-)-5-(1-carboxy-ethoxymethyl)-isophthalic acid trisodium salt), have been hydrothermally synthesized through the reaction of Na3L with divalent cadmium salts with, or without the presence of ancillary nitrogen ligands (bpp = 1,3-bi(4-pyridyl)propane, p-bix = 1,4-bis(imidazol-1-ylmethyl)benzene, m-bix = 1,3-bis(imidazol-1-ylmethyl)benzene, dpa = 4,4'-dipyridylamine, bpbd = 2,3-bis(4'-pyridy1)-2,3-butanediol)). Complex 1 is a threedimensional (3D) framework and displays a (4,8)-connected framework with {4(12).6(12).8(4)} (flu) topology. 2 features a 3D architecture too, in which the one-dimensional (1D) (Cd-bpp), helical chains are alternately arranged in a right- and left-handed sequence. Complex 3 exhibits a homochiral 3D framework and is a new (3,8)-connected net with a Schlafli symbol of {4.5. 6}(2){4(2).5(6).6(18).7.8} topology. Complex 4 bears a homochiral layered structure, which is united together to generate a 3D supramolecular structure through interlayer C-H center dot center dot center dot O and C-H center dot center dot center dot pi interactions. Interlayer C-H center dot center dot center dot pi and N-H center dot center dot center dot N interactions led layered complex 5 to a 3D supramolecular architecture. Complex 6 shows a new (3,5,6)-connected net with a Schlafli symbol of {4.6(2)}(2){4(2). 6(10). 8(2).10}{4(2).6(6).8(2)}(2) J topology. Complexes 3 and 4 crystallize in the chiral C2 space group, and their circular dichroism spectra exhibit obvious positive or negative Cotton effects. Moreover, 3 and 4 are second-harmonic generation (SHG) active, and the SHG efficiency is 0.5 and 0.4 times as much as that of urea, respectively.