ing at the problem of difficult adjustment of prism-grating-prism (PGP) imaging spectrometer, the method of correcting the chromatic aberration of PGP imaging spectrometer is used to ensure that the detector image plane is perpendicular to the optical axis, and a wide-band achromatic PGP system is designed in this paper. Starting from the wide-band apochromatic theory, the minimum theoretical chromatic aberration of the three glass material combinations is calculated, which provides theoretical support for the apochromatic optical design. Using the optical design software to optimize the initial structure, the results show that the secondary spectrum of the PGP system has been well corrected, and the CCD of the detector does not need to be tilted, which is more convenient for later installation and adjustment. The coverage spectrum width is 400--1000 nm, the field of view is 9.2 mm, the spatial resolution is better than 10 μm, the spectral resolution is better than 2.8 nm, and the optical transfer function is greater than 0.7, which is close to the diffraction limit, meeting imaging requirements.