A porous metal-organic framework [C₂₁H₂₀CoF₆O₇] was synthesized with Co(CH₃COO)₂·4H₂O and CPHFP (2,2΄-bis(4-carboxyphenyl)hexafluoro-propane) under hydrothermal conditions. This FMOF-Co has been characterized by elemental analysis, infrared spectroscopy, thermogravimetric analysis, single-crystal and powder X-ray diffraction. The crystal is of monoclinic space group P2₁/n with a = 7.8911(2), b = 29.9053(8), c = 10.5811(3) Å, β = 90.193(10)°, V = 2499.70(12) ų, Z = 4, M_r = 557.3, D_c = 1.481 g·cm^–3, F(000) = 1132, μ = 0.768 mm^–1, GOOF = 1.035, the final R = 0.0722 and wR = 0.2326 for 6347 observed reflections with I > 2σ(I). The structure of FMOF-Co is constructed form the linkage of Co(II) through CPHFP, forming a 3D net framework. The Kr and Xe uptake values are 0.225 and 0.484 mmol·g^–1 at 303 K (100 KPa) with their mol selectivity to be 0.46; while the Kr and Xe uptake values are 0.486 and 0.077 mmol·g^–1 at 233 K (100 KPa), with their mol separation being 6.29 at this condition.