Three new zinc coordination polymers, namely {[Zn(4-pmntd)Cl2]·H2O}n (1), {[Zn(4-pmntd)(CH3CN)4]·(ClO4)2·H2O}n (2), and {[Zn(4-pmntd)(H2O)4]·(CF3SO3)2·3H2O}n (3) (4-pmntd = N,N′-bis(4-pyridylmethyl)-naphthalene diimide) have been synthesized by reactions of 4-pmntd with ZnCl2, Zn(ClO4)2, and Zn(CF3SO3)2, respectively. Compound 1 is an unusual one-dimensional (1D) single-stranded double helical chain containing tubular channels; 2 is an uncommon 1D zigzag chain arranged in a cross-like fashion to generate a 3D plywood-like array; 3 is a typical 1D zigzag chain arranged in a parallel array containing 1D quadrangle channels to accommodate the counter anions and water molecules. The structural diversity in these compounds is attributed to different coordination abilities, sizes, and geometries of counter anions. The anion exchange property of 3 was investigated.