Performance differences between Offner convex grating imaging spectrometer and Dyson concave grating imaging spectrometer, both with concentric structure, was analyzed under different grating constants. The diffraction angle expressions of the two spectrometers were obtained, and their diffraction characteristics were acquired. Both of the spectrometers were designed and analyzed by ZEMAX, under F number of 2.5, spectral rage of 8-12 μm, spectral resolution of 15.6 nm, and grating constants of 100 μm and 50 μm. The two structures could both meet the system requirements using spherical mirrors in the case of a higher grating constant. Offner′s volume is 7 times larger than Dyson′s, and Offner′s weight is about Dyson′s 1/13. When grating constant turned lower, Dyson could still meet the requirements just with spherical mirrors, while Offner must adopt aspherical mirrors and make an off-axis design for the requirements. The Offner′s volume is 7 times larger than Dyson′s, and Offner′s weight is about Dyson′s 1/11. The results show that Offner form and Dyson form have advantages and disadvantages in the aspect of operability of machining, volume, and weight. In the selection of spectrometer, the choice should be made depending on the specific application requirements.