A two-dimensional coordination polymer [Sm(BCBI)(NO3)2·H2O]n (Sm-BCBI) was obtained by the reaction of 1,3-bis(4-carboxybenzyl)-benzimidazolium chloride (H2BCBI) with samarium nitrate under hydrothermal conditions. The N-heterocyclic carbene-silver functionalized samarium coordination polymer (NHC-Ag(I)@Sm-BCBI) was prepared by the reaction of Sm-BCBI with AgOAc to introduce the NHC-Ag(I) catalytic sites. Sm-BCBI and NHC-Ag(I)@Sm-BCBI were characterized by single crystal X-ray diffraction, PXRD, TGA, XPS, ICP-OES, SEM and EDS. The results show that Sm-BCBI is a two-dimensional layer structure; the NHC-Ag(I)@Sm-BCBI catalyst has good thermal stability, and the silver in the catalyst exists in the form of +1 valence. The catalyst was applied to the carboxylation reaction of CO2 (0.1 MPa) with phenylacetylene to generate phenylpropiolic acid. Under the optimum reaction conditions of reaction temperature 50 °C, Cs2CO3 as base, DMF as solvent, NHC-Ag(I)@Sm-BCBI catalyst 70 mg (0.35%) and reaction time 16 h, the separation yield reaches 80%. The catalyst is easy to recycle, and the catalytic yield can still reach 60% after 4 cycles.