The incorporation of Lewis acid-base sites in catalysts has been considered as a significant approach to fabricating bifunctional catalysts with efficient catalytic activity for CO2 fixation. In this paper, a series of Hafnium-based metal-organic frameworks (Hf-MOFs), NU-912(Hf) and NU-912-X(Hf)-X (X = -NH2, -Br, -CN, and -I) derivatives assembled by Lewis acidic Hf6(μ3-O)4(μ3-OH)4(H2O)4(OH)4 (Hf6) clusters and Lewis base-attached organic linkers, are successfully synthesized by a facile ligand functionalization method. These isostructural Hf-MOFs, which exhibit diamond channels of 1.3 nm diameter, great chemical stability, and CO2 adsorption capacity, have been evaluated as catalysts for the CO2 cycloaddition reaction with epoxides. Catalytic experiments reveal that the micropore environments of these MOFs have an outstanding impact on catalytic activity. Remarkably, NU-912(Hf)-I serves as an efficient heterogeneous catalyst for this catalytic reaction under mild conditions due to the high density of Lewis acid Hf6 cluster centers and strong Lewis base functional groups, surpassing most of the reported MOF-based catalysts.