A specific imaging spectrometer based on concentric offaxis dual reflector system was proposed which consisted of four spherical mirrors and a plane grating. On the basis of analysis of the concentric offaxis dual reflector system, aberration theory and optical pathlength concept were used to derive an expression for the separation of astigmatic images in concentric offaxis dual reflector system, the astigmatism elimination in which was found further. It is shown that the astigmatism of the imaging spectrometer can be eliminated by applying concentric offaxis dual reflector system without astigmatism in both the collimating and condensing optics. A symmetrical and concentric imaging spectrometer was described and a generalized design procedure was shown. The symmetrical and concentric imaging spectrometer working in farultraviolet (120~180 nm) wavelength was simulated by applying the design procedure. To verify the stigmatic principle, spot diagram and the curves of astigmatism were shown. The results show that the initial structure satisfies the stigmatic principle well. The spectral resolution of the optimized spectrometer is close to 1.6 nm and the modulation transfer function is more than 0.37 for the total field of view at all wavelengths, which provides good imaging quality.