A novel edge-filter wavelength demodulation technique based on the special spectral characteristics of chirped fiber grating and long-period fiber grating was proposed in this paper, which offers a fast wavelength demodulation method for interferometric and resonance fiber-optic sensors. In this wavelength demodulation system, the chirped fiber grating acts as a rectangular filter, which extracts one interferometric peak out of the periodic interference spectrum; The long-period fiber grating acts as an edge filter, whose transmission profile is shown to be nearly linear over a sufficiently wide range, converting the wavelength variation into optical power in a linear relationship, that the wavelength can be acquired through optical power measurement. The demodulation range can go up to one free spectrum range (FSR) and the demodulation speed is determined by the response of the photodetector theoretically. This demodulation technique has practical significance with the fast demodulation speed, wide demodulation range, low cost, small size, and the convenience to multichannel extension. The principle and structure of the demodulation system were illustrated in detail, and the experiment was setup through applying the demodulation system to an interferometric fiber optic current sensor. Experiment result showed the system could demodulate accurately and fast when the sensor was under power current and pulse current. This paper is of great significance for promoting the engineering practical level of interference and resonance fiber optic sensors.