Synthetic conditions and ligands are the key structural defining factors of metal–organic frameworks (MOFs). Therefore, reasonable optimization of these aspects is considered to be an effective means for designing materials with novel structures and target functions. Herein, two novel Co(II)-based MOFs, namely [Co(HL)(dibp)]n (HL-8) and {[Co2(L)(OH)(dibp)]·DMA}n (HL-9) (H3L = 2′,6′-dimethyl-[1,1′-biphenyl]-3,4′,5-tricarboxylic acid; dibp = 4,4′-di(1H-imidazol-1-yl)-1,1′-biphenyl]), have been hydrothermally synthesized and structurally characterized. HL-8 crystallizes in the orthorhombic system (Pna21) with a grid layer structure, while HL-9 crystallizes in the monoclinic P21/n space group assembled through Co4(OH)2 clusters with organic ligands. Remarkably, benefiting from the finite cage-like structure, HL-9 exhibited enhanced performance in carbon dioxide (CO2) adsorption/catalytic transformation and excellent size selectivity during dye molecular adsorption process.