In this study, we have synthesized two zinc(II)-based metal-organic frameworks (MOFs) designated as [Zn(4-nvp)(bdc)]·(MeOH) (1) and [Zn2(4-nvp)2(bpdc)2]·(DMF) (2) [4-nvp = 4-(1-Naphthylvinyl) pyridine, H2bdc = 1,4-benzendicarboxylic acid and H2bpdc = 4,4'-biphenyldicarboxylic acid]. Single-crystal X-ray diffraction (SCXRD) of both compounds unveiled an interesting paddle-wheel [Zn2(O2C-C)4] secondary building unit composed of dinuclear Zn (II) centers and four dicarboxylate groups with a (4,4) square grid topology. These SBUs are interconnected giving rise to an infinite 2D layer architecture. Notably, the grid structure is composed of MeOH molecules in compound 1 and DMF molecules in compound 2, both of them arranged in a free lattice. In both compounds, 3D supramolecular architecture is ultimately formed through the stacking of 2D layers. Since the length of the bpdc ligand is higher than that of the bdc ligand, the solvent-accessible void volume is comparatively higher for compound 2. To corroborate all non-bonded interactions, Hirshfeld analysis was carried out for synthesized compounds. DNA binding application was extensively investigated through docking study. Results indicated that the synthesized compounds have strong affinities towards DNA via DNA groove binding. Henceforth, the synthesized compounds 1 and 2 would open the door for their potential applications as particular protein binders and bioactive substances.