Snapshot spectral imaging systems can obtain spectral images of moving targets in real time, and have urgent application requirements in the field of dynamic target tracking and recognition. The spectral and spatial resolutions of the snapshot spectral imaging system are mutually restricted. The existing snapshot spectral imaging system has a small numerical aperture, and it is difficult to achieve high spectral and spatial resolutions at the same time. This paper proposes a novel snapshot spectral imaging system based on the Dyson concentric structure. It has the advantages of large numerical aperture, excellent imaging performance, and compact structure. Meanwhile, through the off-axis of the field of view and complex design, the optical imaging performance is maintained while the space for mechanical assembly and adjustment is increased, which has good engineering feasibility. The optimized design of the novel snapshot spectral imaging system has a numerical aperture of 0.3, a spectral resolution better than 0.54 nm, and a spatial sampling point number of 112×24. This kind of high spectral and spatial resolution snapshot spectral imaging system can provide an important theoretical basis for the study of the snapshot spectral imaging system for the accurate detection and recognition of fast moving targets in a large field of view.