A space-borne differential optical absorption spectrometer was designed on the basis of a four channel Offer imaging spectrometer with a convex grating. It could acquire high accuracy radiation scattered by earth surfaces or air in a nadir push-broom mode, and could quantitatively obtain the trace gas distribution based on the “fingerprint” absorption of the trace gas at different spectral information and the differential optical absorption spectrum algorithm. According to the characteristics of large field, wide wavelength range, high spatial and spectral resolution of the spectrometer, the corresponding methods of spectral calibration and radiometric calibration were presented, and a calibration system was built. Then the spectral and radiometric calibrations of the spectrometer were realized, and the calibration uncertainty was analyzed. Experimental results show that spectral calibration uncertainty of the instrument is 0.027 nm and the radiation uncertainty is 2.96%. The calibration accuracy meets the given requirements and can provide a foundation for quantitatively inversion of the instrument.