Traditional spectral recovery on interferometric spectrometer uses the Fourier transform to recover spectrum. In order to eliminate the influence of side lobes caused by finite optical path difference on the spectral recovery accuracy, it performs interferogram apodization, but that decreases the spectral resolution of the recovery spectrum. In order to ensure the spectral resolution and improve the spectral recovery accuracy, in this paper, a spectral recovery method on Sagnac interferometric spectrometer based on instrumental eigen matrix is presented. The method is designed to construct an instrumental eigen matrix for every interferometric spectrometer system by laboratory calibration and theoretical derivation, and uses it to recover spectrum by least squares method. The spectra of various substances were used to perform the simulation experiments to test the spectral recovery accuracy of the two spectral recovery methods. The results indicate the recovery error of the instrument matrix method is stabilized at 1%~3%, and that of the Fourier transform method is 3%~7%. The experiments testify that the spectral recovery accuracy using the spectral recovery method based on instrumental eigen matrix is better than that using the Fourier transform spectral recovery method.