The working principle, structure characteristics and advantages of the optical system in an Offner imaging spectrometer are introduced based on a concentric structure. The research and development of the Offner imaging spectrometer are overviewed. It describes in detail the commonly used three kinds of correction aberration ways, namely by changing optical element adjustable structure to correct the aberration, by aberration theory analysis based on single grating to correct the aberration and by design of a convex holographic grating to improve the resolution of the spectral image. Then, it summarizes the key problems of the Offner imaging spectrometer and emphasizes some of them should be solved in further, such as correction of the system aberration, improvement of spectral resolution and spatial resolution and enhancement of detecting weak signals. Finally, it points out that the development trend of the system is higher resolution, better detecting capability and more compact structure. Based on the research of the Offner imaging spectrometer, this paper proposes an approach to correct aberration based on the integrated design of convex holographic grating and spectrometer.