Ring-opening　copolymerization　(ROCOP)　of　epoxide　with　cyclic　anhydride　plays　critical　role　in　the　preparation　of　polyesters.　Herein,　the　UiO-type　MOFs　including　UiO-66,　UiO-66-NH2,　UiO-66-NO2,　UiO-66-Br　and　UiO-67　with　octahedral　morphology　were　synthesized　by　different　ligands　and　used　as　heterogeneous　catalysts　for　ROCOP　of　epoxide　with　cyclic　anhydride.　It　was　shown　that　the　UiO-67　with　ultra-high　specific　surface　area　and　large　pore　size　endows　it　with　abundant　of　catalytic　active　sites　and　the　highest　catalytic　activity,　which　makes　UiO-67　present　seven　times　higher　turnover　frequency　(192.6　h-1)　than　that　of　UiO-66　(23.6　h-1)　under　the　same　conditions.　Besides,　the　strong　electron-absorbing　group　enhances　the　catalytic　activity　of　UiO-type　MOFs.　The　cycling　test　proves　that　the　UiO-67　has　good　recoverability　and　there　was　no　significant　loss　of　catalytic　activity　after　been　reused　for　three　times.　The　kinetic　study　showed　that　the　ROCOP　of　epoxide　with　cyclic　anhydride　catalyzed　by　UiO-67　was　a　first-order　kinetic　reaction,　and　its　apparent　activation　energy　(Ea)　was　about　71.75　kJ　center　dot　mol-　1　calculated　by　the　Arrhenius　equation,　which　was　27.5%　lower　than　that　of　UiO-66　(98.94　kJ　center　dot　mol-　1).