Reactions of Zn(NO3)2 with tetrakis(4-pyridyl)cyclobutane (tpcb) and 1,4-benzenedicarboxylic acid (1,4-H2BDC), 4,4′-biphenyldicarboxylic acid (4,4′-H2BPDB), 5-methyl-1,3-benzenedicarboxylic acid (5-CH3-1,3-H2BDC), 1,3,5-benzenetricarboxylic acid (1,3,5-H3BTC), 5-amino-1,3-benzenedicarboxylic acid (5-NH2-1,3-H2BDC), 4,4′-benzophenonedicarboxylic acid (4,4′-H2BPNDB) under solvothermal conditions led to the formation of six polydimensional coordination polymers {[Zn5(1,4-BDC)5(tpcb)2.5]·5H2O}n (1), {[Zn2(4,4′-BPDB)2(tpcb)]·0.5MeCN}n (2), [Zn2(OH2)2(5-CH3-1,3-BDC)2(tpcb)]n (3), {[Zn2(1,3,5-HBTC)2(tpcb)]·H2O}n (4), {[Zn2(5-NH2-1,3-BDC)2(tpcb)·H2O]}n (5), and [Zn2(4,4′-BPNDB)2(tpcb)]n (6). Compounds 1–6 were characterized by elemental analysis, IR, powder X-ray diffraction, and single crystal X-ray diffraction. Compounds 1 and 6 have different 3D (4,4) connected structures. Compounds 2–4 have different two-fold interpenetrating 3D (4,4)-connected structures. Compound 5 holds a 2D (3,4)-connected structure. The solid state luminescent properties of compounds 1–6 at ambient temperature were also investigated. The results provided some interesting insights into ligand effects on the structures and luminescent properties of zinc(II) coordination polymers.