A new ligand, 4-(4-carboxyphenyl)-6-(pyrazin-2-yl)picolinic acid (H2L1), was used to construct four isostructural one-dimensional (1 D) zig-zag chain coordination polymers ([M(L1)(H2O)2]·3H2O, M = Mn (1), Co (2), Cd (3) and Zn (4)). Moreover, when changing the ligand substituent group from pyrazine ring to furan ring, another new ligand, 4-(4-carboxyphenyl)-6-(furan-2-yl)picolinic acid (H2L2), was synthesized. Based on H2L2, different structural 1 D coordination polymers, ([Mn(L2)(H2O)2] (5) and [Ni(L2)(H2O)2]·H2O (6)), have been obtained under the same solvothermal conditions as for the syntheses of isostructural 1–4. Interestingly, only through changing the ligand substituent group, the 1 D isostructural zig-zag chain (1–4) was adjusted to a 1 D molecular box chain (5) and 1 D linear chain (6), which should be ascribed to ligand substituent group effects. The various 1 D chain structures originate from the types of ligand substituent group: the substituent group with a pyrazine ring only yields isostructural coordination polymers 1–4, whereas the substituent group with a furan ring can construct different structural coordination polymers, such as a 1 D molecular box chain (5) or a 1 D linear chain (6). The photoluminescent properties of all coordination polymers were also examined.