Introduces a Fourier transform spectrometric method for the precise characterization of dispersion of chirped FBGs(fiber Bragg grating). The measurement system is a fiber Michelson interferometer composed of a broadband EDFA (Erium doped fiber amplifier) light source, a 3db 2×2 fiber coupler, a pair of polarization controllers, a optical attenuator, a fiber filter, an O/E converter, A/D converter, computer and a optical path difference (OPD) scanning system. The digital interferogram of the system is acquired by recording the electric signal produced by the O/E converter through the A/D converter and by computer during the scanning of OPD. The recorded interferogram is then manipulated through a process involving low-pass filtering, fast Fourier transformation, phase unwrapping and computation of the numerical differentials of the unwrapped phase to the wavelength so as to obtain the relative group delay of the chirped FBG under test. It is proved by practical experiments that the repeatability of the system is up to Ps(picosecond) magnitude order.