The efficient transformation of carbon dioxide into useful chemical feedstock is of great significance, attracting intense research interest. The widely studied porous-coordinated polymers possess large pores to adsorb guest molecules and further allow the contact and to transfer the substrate molecule within their microenvironment. Here we present the synthesis of a silver-based metal-organic frameworks (MOFs) material with a three-dimensional structure by incorporating a tetraphenyl-ethylene moiety as the four-point connected node via the solvothermal method. This polymer exhibits as an efficient heterogeneous catalyst for the carboxylative cyclization of CO2 to α-methylene cyclic carbonates in excellent yields. Moreover, the introduction of silver (Ag (I)) chains in this framework shows the specific alkynophilicity to activate C≡C bonds in propargylic alcohols to greatly accelerate the efficient conversion, and the large pores in the catalyst exhibit a size-selective catalytic performance.