The metal-organic frameworks UiO-66 with single or binary -(OH)2 and -NO2 functional groups were synthesized, and their structures and properties were characterized by Fourier transform infrared spectroscopy, X-ray diffraction, thermogravimetric analysis, scanning electron microscopy, and nitrogen adsorption isotherms. Their performances in CO2 and CH4 adsorption at high pressures and different temperatures (273 and 298 K) were also determined. Singly functionalized UiO-66-(OH)2 had a lower thermal stability than UiO-66-NO2, but the thermal stability of binary UiO-66-(OH)2-NO2 significantly improved to 650 K. The binary-functionalized samples UiO-66-(OH)2-NO2 and UiO-66-NO2-(OH)2 displayed higher CH4 and CO2 adsorption than UiO-66-(OH)2 and UiO-66-NO2. The CO2 adsorption capacities of UiO-66-(OH)2-NO2 and UiO-66-NO2-(OH)2 were 4.65 and 7.35 mmol/g, respectively, at 273 K and 900 kPa. UiO-66-(OH)2 had a higher separation factor for selective separation of CO2 from CH4, especially at low pressures up to 100 kPa; the separation factor ranged from 4.9 at about 100 kPa to 5.8 at 60 kPa.