This article introduced the needs and key technologies of the Far Ultraviolet (FUV) imaging spectrometer. The design method and spectral calibration were researched. The FUV imaging spectrometer was based on crossed Czerny-Turner optical structure with all reflective components in it. The initial structure was calculated based on the primary aberrations theory, and the optical system whose effective wavelength range is from 100 nm to 300 nm was simulated and optimized by the optical design software Zemax in order to advance the spectral resolution. The crossed Czerny-Turner spectrometer system was set up and the spectral calibration and imaging ability test were achieved. The measured spectral bandwidth is less than 1.67 nm.