A highly sensitive gas refractive index (RI) sensor based on hollow-core photonic bandgap fiber (HC-PBF) and Fourier transform white-light interferometry was experimentally demonstrated. HC-PBFs with lower loss than hollow silica tubes render a longer air cavity for the Fabry-Perot interferometers (FPIs) without a great deal of compromise to the fringe visibility of interference. Fourier transform phase demodulation method was employed in the experiment and a directly proportional relationship between the phase sensitivity and cavity length was demonstrated. For a cavity length of ∼24.9 mm, the sensor's gas RI sensitivity reaches up to 50775.54 µm/RIU in an air RI range from 1.000 to 1.030. Considering the cavity length demodulation resolution of 0.06 µm achieved by this method, the sensor can detect gas RI change with a resolution of 10 RIU, which can meet the sensing demand for almost all the gases. Moreover, the gas RI sensitivity and measurement range can be improved further by lengthening the HC-PBF. The high sensitivity, large dynamic range and good linearity of the proposed sensor make it a good candidate for biosensing, monitoring of modern chemical industry or gas laser systems.