A high speed quasi-distributed demodulation method based on the microwave photonics and the chromatic dispersion effect is designed and implemented for weak fiber Bragg gratings (FBGs). A broadband light modulated with a frequency-swept microwave is reflected by FBGs, and the reflected signal mixes with the original microwave to. In this paper, a novel demodulation algorithm based on the variable-step-size method and cross-correlation algorithm is proposed to demodulate the wavelength of an FBG. With the help of a wavelength-swept laser, the reflection spectrum and transmission spectrum of an FBG can be mapped into two pulse signals with opposite.