In order to improve the Fourier spectrometer spectral calibration accuracy and reduce spectral calibration error, we studied the Fourier spectrometer spectral calibration algorithm. The study is based on the data of spectral calibration experiment of the atmospheric vertical detector, which is a payload of FY-4 meteorology satellite. Firstly, the spectroscopic principle of the Fourier spectrometer is analyzed. Secondly, after analyzing the principle of the spectrum shift caused by the reference laser wave number drift, the light off-axis, and the limited field of view, the Fourier spectrometer spectral calibration formula and the calibration parameter calculation method are obtained. Then, the reasons for the large spectral calibration error caused by the barrier effect of Fast Fourier Transform(FFT) and the toe function generated by the truncation of the interferogram are analyzed. By comparing several different spectral refinement methods, fast Chirp Z-transform(CZT) for spectral refinement is selected to solve the problem of lower spectral resolution of FFT resulting in larger spectral error. Gaussian expansion and convoluting the sinc function of reference gas spectral can reduce the calibration error caused by limited optical path difference. At last, the spectral calibration algorithm is validated by using experimentally measured data. By comparing the calibration errors before and after refining the spectra using CZT, and the calibration errors before and after the processing of the reference gas spectrum, the algorithm is proved to be effective in improving spectral calibration accuracy. Spectral calibration error can be reduced about 10 times at most.