In order to meet the requirements of wide-band hyperspectral Czerny-Turner spectrometer, based on the aberration theory, on the one hand, the astigmatism generated by the grating is used to compensate the astigmatism of the spherical mirror, and on the other hand, the opposite astigmatism is introduced through cylindrical mirror to compensate for the residual astigmatism, so as to achieve the full range elimination of astigmatism, and at last to improve the resolution of the Czerny-Turner structure spectrometer imaging system. Firstly, the basic formulas of grating and cylindrical mirror to compensate for astigmatism is deduced, and then based on this, the Czerny-Turner spectrometer imaging system with full-band astigmatism in the band of 900-1700 nm and 1700-2500 nm are designed respectively. Finally, the two parts are combined through the front optical path, thus realize the astigmatism Czerny-Turner structure spectrometer imaging system in the full range of 900-2500 nm. The full-band resolution of the spectrometer is less than 10 nm, the object-side numerical aperture is 0.07, and the full-band root mean square radius is less than 4 μm. The optimization analysis of ZEMAX shows that the designed spectrometer not only meets the astigmatism elimination requirements in the whole band, but also has good imaging quality.