A solvothermal reaction of CuI with a bifunctional organic ligand 3,5-pyridinedicarboxylic acid (H2pdc) afforded a novel heterovalent copper-organic framework, [(CuI2)Cu(pdc)4(H2O)4]·4DMSO (1) (DMSO = dimethyl sulfoxide). Compound 1 was structurally characterized by single-crystal X-ray diffraction analyses and further characterized by infrared spectroscopy (IR), powder X-ray diffraction (PXRD), elemental analyses and thermogravimetric analyses (TGA). Structural analysis indicates that two kinds of common secondary building units (SBUs) coexist in this 3D network. The linkage of Cu+ and I- generates [CuI2] subunits and the connection of Cu2+ with carboxyl-O atoms gives rise to binuclear paddle-wheel [Cu(COO)4(H2O)2] moieties. In compound 1, two different SBUs are bridged with pdc2- ligands to construct a micro-sized cage with an internal spherical cavity. Through a cage-to-cage connection, the 3D porous framework is formed which features intersecting 1D channels. Gas sorption measurements were conducted on the activated 1, showing a H2 uptake of 1.46 wt% at 77 K and under 1 bar with a high initial adsorption enthalpy of 8.2 kJ mol-1. Moreover, compound 1 has excellent adsorption selectivity for CO2 over N2 and CH4.