Three Cu(II) coordination polymers (CPs), [Cu3(L1)4(OH)2(H2O)2]n (1), [Cu(L2)(OH)]n (2) and [Cu(L2)(CH3O)]n (3), are synthesized by solvothermal method using nicotinate N-oxide (HL1) or isonicotinate N-oxide (HL2) as organic ligands and Cu(OAc)2·H2O as metal salt. Their structures and properties are characterized by single crystal X-ray diffraction, X-ray powder diffraction, infrared spectroscopy, elemental analysis, thermogravimetric analysis and ultraviolet spectroscopy. CP 1 shows one-dimensional (1D) wavy double chain, CP 2 shows two-dimensional (2D) wavy double layer, CP 3 shows three-dimensional (3D) microporous structure with 1D wavy channels. CPs 1-3 are synthesized under similar solvothermal conditions, but show a multi-dimensional configurations, indicating that the relative position of functional groups in ligand, the coordination mode of ligand and the solvent system all play important roles in the structural diversity of CPs. Thermogravimetric analysis shows that CPs 1-3 have good thermal stability, and the stability is 1 < 2 < 3, indicating that the higher the dimension of CPs 1-3, the better the thermal stability. Nitrotetrazolium blue chloride (NBT) photoreduction test shows that CPs 1-3 have certain superoxide dismutase (SOD) activity, and the activity is 1 > 2 > 3, indicating that the lower the dimension of CPs 1-3, the better the SOD activity. The lower IC50 values of CPs 1 and 2 indicate that they can be used as potential SOD mimetics.