Today, due to the momentary release of carbon dioxide and increasing global heat, solutions that prevent the release of this greenhouse gas into the atmosphere are very important. In this work, a nanoporous sorbent with a 3D framework and chemical formula of [Ca1.5(FDC)1.5(DMF)] (MUT-13) (FDC2–= furan-2,5-dicarboxylate, DMF= N,N-dimethylformamide) was prepared in different synthetic routes. Single crystal of MUT-13 was identified by X-ray crystallographic analysis and other physicochemical analyses. Then, with the help of GCMC, the performance of MUT-13 was simulated in the adsorption of various gases (CO2, H2, C2H2, CH4, and N2) under different temperature and pressure conditions. Also, the potential of MUT-13 in separating carbon dioxide from binary mixtures (CO2/CH4, CO2/N2, CO2/H2 and CO2/C2H2) was investigated. The results indicated that the sorption structure has a high capacity to adsorb carbon dioxide (6.2 mmol.g–1) and acetylene (5.5 mmol.g–1) molecules in environmental conditions. It also shows a separation greater than 5000 and 2000 for the mixture of CO2:H2 at low and high pressures, respectively. This good performance of MUT-13 in adsorbing and separating carbon dioxide compared to other MOF-based adsorbents can be related to the surface of its pores decorated by the heteroatom of the ligand and the presence of unsaturated metal centers in its structure.