Wavelength-swept laser technique is an active demodulation method which integrates laser source and detecting circuit together to achieve compact size. The method also has the advantages such as large demodulation range, high accuracy, and comparatively high speed. In this paper, we present a FBG interrogation method based on wavelength-swept Laser, in which an erbium-doped fiber is used as gain medium and connected by a WDM to form a ring cavity, a fiber FP tunable filter is inserted in the loop for choosing the laser frequency and a gas absorption cell is adopted as a frequency reference. The laser wavelength is swept by driving the FP filter. If the laser wavelength matches with that of FBG sensors, there will be some strong reflection peak signals. Detecting such signals with the transmittance signal after the gas absorption cell synchronously and analyzing them, the center wavelengths of the FBG sensors are calculated out at last. Here, we discuss the data processing method based on the frequency reference, and experimentally study the swept laser characteristics. Finally, we adopt this interrogator to demodulate FBG stress sensors. The results show that, the demodulation range almost covers C+L band, the resolution and accuracy can reach about 1pm or less and 5pm respectively. So it is very suitable for most FBG measurements.