Hyperspectral monitor on CarbonSat focuses on the detection of vegetation carbon sink and forest stock in the terrestrial ecosystem by detecting the spectrum of 670~780 nm, mapping the temporal and spatial distribution vegetation fluorescence to meet the needs of global carbon sink quantitative monitoring and forest vegetation productivity assessment. How to effectively calibrate the spectral parameters of HSM, establishing the relationship between the detector and the measured spectral information is the basis of quantitative inversion is the basis of quantitative radiance inversion. This paper gave the spectral data error model of HSM by grating equation, combined with the spot distribution function of the optical system, the Instrument Line Shape (ILS) of HSM is obtained. The simulation results show that the ILS changes slowly, and the ILS is approximately the same in a small spectral range. The wavelength error is mainly caused by grating manufacturing. It can be eliminated by the spectral line calibration method. In order to realize the spectral calibration of HSM on the ground, a calibration system that includes the tunable laser, wavelength meter, and rotating engineering diffuser is established in the vacuum tank. A monochromatic light with a linewidth less than 0.001 nm is provided, and the automatic data processing program is used to test the relationship between the response curve of the detector and the monochromatic light. The spectral sampling rate of HSM is about 2.5 pixels, and the effective data points of the single wavelength spectrum are limited. For getting accurate data of ILS, the spectral sampling rate is increased by two orders of magnitude by wavelength scanning at 0.015 nm wavelength interval, and the spectral resolution is obtained by Gaussian fitting. The results show that the spectral resolution of the HSM is 0.24~0.26 nm. The wavelength calibration data of all pixels is obtained by selecting the characteristic wavelength and cubic polynomial fitting. The characteristic wavelength is selected to verify the fitting residual. The results show that the calibration accuracy is better than 0.005 nm. In order to further verify the spectral calibration results, the ground push broom imaging experiment of HSM was carried out. The spectral data of pine forest and gravel pavement were obtained at the Huailai test station of the Aerospace Academy of the Chinese Academy of Sciences. The comparison results between the atmospheric absorption line measured by HSM and the atmospheric absorption line of HITRAN show the deviation of the central wavelength of the oxygen absorption line is less than 0.003 nm. The calibration result satisfied the system requirement HSM.