An optical system working in 120~180 nm is developed for the study of ionospheric imaging spectrometer carried by satellite in China. The scheme, that the telescope is an off-axis parabolic mirror and the imaging spectral system is a single toroidal grating, is assumed with comparing different programs in foreign countries, based on characteristics of targets. Then the theory is studied by introducing the surface equation of the grating and optical path function, to get a novel broadband aberration-corrected method to resolve the disadvantages of traditional single grating structure, non-homogeneous aberration correction and low spatial resolution. The original structure is obtained by Matlab and is simulated by Zemax. A system operating in 120~180 nm with F-number of 6.8, focal length of 102.3 mm is designed. This imaging spectrometer has high spatial resolution and spectral resolution. The results demonstrate that aberrations are totally corrected, the modulation transfer function (MTF) of all field of view is more than 0.7 in the waveband, and the spectral resolution is 0.56 nm. It proves that the design which can satisfy the requirement of the design specifications is more convenient and more predominant.