A novel metal-organic framework [Co(BTTA)(H₂O)₂]_n (FJI-H24) has been prepared from H₂BTTA ligand and CoCl₂, and its structure was determined by single-crystal X-ray diffraction, thermogravimetric analysis, and Fourier transform infrared spectroscopy. It has relatively narrow pores and high density of open metal ions and free Lewis base sites. Gas adsorption tests demonstrate that FJI-H24 has moderate CO₂ (34.0 cm³·g^–1) and C₂H₂ (53.0 cm³·g^–1) adsorption capacity, but displays high selectivity of CO₂/N₂ (87) and C₂H₂/CH₄ (66) under ambient conditions (298 K, 1 atm), which may be attributed to its relatively narrow pores and polar environment. This work will provide a potential strategy for preparing practical porous metal-organic frameworks for gas adsorption and purification.