To improve the wavelength calibration accuracy of multi-channel grating scanning spectrometers, the principle of linear wavelength scanning of traditional single-channel grating spectrometers is first introduced. Then, the theoretical nonlinear relationship between the spectrometer''s output wavelength and the moving distance of the lead screw is derived based on the common grating axis error. Given the nonlinear relationship, wavelength calibration of a prototype of Fengyun-3 solar irradiance spectrometer is performed. The results demonstrate that the calibration accuracy of the traditional calibration is 0.08 nm,and the calibration accuracy is increased to 0.03 nm by using the wavelength nonlinear formula. This result satisfies the requirements of the instrument''s specifications. Thus, the wavelength nonlinear relationship of a multi-channel grating scanning spectrometer is verified.