Abstract: Hyperspectral imaging detection technology involves optics, spectroscopy, machinery, microelectronics, computer and other disciplines. The design of imaging spectrometer should be compact and apochromatic. Based on the aberration theory, theoretical formula of secondary spectrum was derived according to the dispersion characteristics of typical glass materials in 400 nm~1 000 nm. For a system with FOV of 7.63, F/# =5, f= 60 mm, its secondary spectrum was corrected in design with ZEMAX software. The results indicate the MTF of the imaging system is greater than 0.5 at 60 lp/mm in visible and infrared band, other aberration requirements are met as well.