Dispersive imaging spectrometers that use back-illuminated CCDs have interference fringes in near-infrared band. These fringes are sensitive to the distribution of incident light wavelength and stable in spatial frequency. Therefore, they are very suitable for measuring and calibrating spectral deviation. In this paper, we built a grating dispersion push-broom imaging spectrometer prototype. We then estimated the distribution law of fringes and use band-pass filter and least squares method to extract the phase information of the interference fringes. Finally, we calculated the spectrum offsets based on this information. Experiments show that when the incident light intensity changes by more than 130%, the maximum uncertainty of fitting line positions is 0.0073nm. We change the spectral position and compare the spectral deviations calculated by using fitting algorithm and measured by using mercury spectrum. The maximum error of spectral position is 0.1358nm. Our fitting algorithm can effectively reduce dependence on light stability of the calibration system, and improve detection accuracy for slight offsets in spectral dimension.