The invention relates to a fiber bragg grating demodulating device and method based on chromatic dispersion Mach-Zehnder interferometry. The fiber bragg grating demodulating device comprises a broadband light source, a narrow-linewidth sweep frequency laser device, a first photoswitch, an optoisolator, a semiconductor optical amplifier, a pulse digital signal source, an optical circulator, a second photoswitch, a reference grating, a sensing grating array, a Faraday rotating mirror, a first optical coupler, dispersion compesation fiber, monomode optical fiber, a second optical coupler, a photoelectric detector set, a data collecting card and an upper computer. The optical fiber dispersion effect and the traditional Mach-Zehnder interferometry are combined to construct chromatic dispersion Mach-Zehnder interferometry, optical path difference caused by the chromatic dispersion effect is used for achieving phase sensibilization, interference information of all gratings in a quasi-distributed fiber bragg grating array is recorded through high-speed time-domain optical pulses, a multi-phase demodulating technology is used for processing time domain interference signals, high-sensitivity and high-speed demodulation of the fiber bragg grating array is achieved, and the demodulating device has the advantages of being high in interference resistance and capable of achieving distributed measurement.