Herein, a novel copper metal–organic framework (MOF), [Cu₂(CPTPTA)(H₂O)]·CH₃NH₃⁺·4H₂O·7NMF (1) (H₅CPTPTA = 5′-(4-carboxyphenyl)-[1,1′:3′,1′′-terphenyl]-3,3′′,5,5′′-tetracarboxylic acid, NMF = N-methylformamide), has been successfully synthesized via solvothermal reaction. By applying a linker desymmetrization strategy, compound 1 was constructed by a reduced-symmetry ligand CPTPTA⁵⁻, leading to three types of channels with various functional sites. Meanwhile, the functional sites promoted the adsorption of CO₂, the uptakes being 123.2(2) and 66.8(2) cm³ g⁻¹ at 273 and 298 K, respectively. Furthermore, the smaller channel exists as two kinds of active sites: Lewis acid sites (LASs) and Brønsted acid sites (BASs); whereas the larger one only exists as LASs. The synergistic catalysis of LASs and BASs makes compound 1 exhibit excellent CO₂ cycloaddition efficiency towards propylene oxide, and the yield can reach 97%. Overall, such a linker desymmetrization strategy can afford an effective approach to synthesize novel functional MOF materials.