The Greenhouse Gases Monitoring Instrument (GMI) is a carbon satellite payload developed based on the principle of spatial heterodyne spectroscopy technology, which is specifically designed for the global analysis of greenhouse gases (CO2 and CH4) “sources” and “sinks”. Due to the low concentration and minimal gradient variations of CO2 and CH4 in the atmosphere, higher precision is required for their retrieval. Vibrations during satellite launch and harsh space environments during on-orbit operation may cause changes in the performance of various payload components, resulting in decreased quality of spectrum products and retrieval precision. This paper proposes a set of on-orbit spectral characteristic evaluation methods tailored for the GMI to monitor the quality of its spectrum. It also develops an adaptive blind pixel detection and correction algorithm specifically for the GMI and optimizes the interferogram processing flow algorithm. On-orbit spectral calibration is performed, and methods to evaluate spectral characteristic parameters have been established. The analysis focuses on the variations of the spectral characteristics in the CO2-1 bands (1.575 μm) of the GMI during one-year of on-orbit calibration spectrum. The initial spectral wavenumber offset is 0.133 cm−1 after entering orbit, and the average spectral wavenumber offset is 0.0313 cm−1 during stable operation. During the one-year period, the maximum variation in the instrumental line shape function of the GMI is 0.006 cm−1. The observed spectrum obtained in nadir observation mode, underwent to accuracy verification. The results demonstrate consistency between the spectral peak wavenumbers and the relative trend changes of the observed and theoretical spectrum, with an average relative residual of 0.987%.