Through use of an irregular pentacarboxylate ligand, 2,2'-(pyridine-2,6-diyl)diterephthalic acid (H4L), two Cu(II)-based metal-organic frameworks, {[(Me2NH2)0.5][Cu0.75(L)0.5(DMA)0.375]·H2O}n (1) and {[Cu4(L)2(H2O)4]·4DMF·8H2O}n (2), have been synthesized. A structural analysis demonstrates that 1 is a 2D layer and 2 shows a 3D framework, which exhibit hopeful possibilities for the selective separations of C2H2/CH4 and CO2/CH4. To enhance the adsorption properties, 5-amino-1H-tetrazole (HAT) has been introduced in the synthesis system, and a new framework, {[Cu4(L)2(ATZ)2(H2O)]·5DMF·5H2O}n (3), has been obtained. 3 is a 3D framework. Especially, 3 is constructed from multiple SBUs and displays an unusual (3,4,6)-connected topology. Furthermore, especially 3 performs better than 1 and 2 in terms of uptake capacity as well as adsorption selectivity, which might be ascribed to the more proper pore space of 3.