Abstract: Infrared imaging spectrometers are applied to volcano behavior detection, forest fire survey, urbanization effect analysis, terrestrial composition and change monitoring, and camouflage recognition. In this paper, based on Dyson relay, a long wave infrared imaging spectrometer with wavelength range of 7.5 to 10 m was designed, which used a concave diffraction grating as its dispersive element. Its F number reached 1.2, field angle of view was 18 and spatial pixel resolution was 1 mrad, spectral resolution was 50 nm and noise equivalent temperature difference (NETD) was less than 0.3 K. The size of this designed optical system was about 72 mm39 mm39 mm, and its modulation transfer function approached to diffraction limitation. It has advantages of high throughput, low inherent aberration, and compactness. Analysis of its stray thermal radiation shows that its own thermal radiation of optical- mechanical system can be effectively suppressed by use of real entrance pupil as cool stop and of cryogenic optics.