A kind of optical system of solar extreme ultraviolet imaging spectrometer is designed aiming at solar extreme ultraviolet imaging spectrometer′s application objective and working environment. The optical system consists of a telescope, a scanning mirror, a slit, a grating and a detector. Wolter typeⅡ configuration is chosen for the telescope, light enter the system by grazing incident, so it has wide working band, and is highly stable, practicable to withstand the rigors of spaceflight. A plane mirror is chosen for scanning mirror, so the imaging quality would not change with scanning angle. A toroidal variedlinespace grating which is 3 600 lines/mm is chosen for dispersion. Compared with toroidal uniformlinespace grating, it superiors in imaging quality, spectral resolution and shortening system length. The working band of the optical system is 17.0~21.0 nm which could meet the probe of the quiet corona in the temperature region 5.8≤log T≤6.3. The field of view is 1228″× 0.8″, the spatial resolution is 0.8 arc sec/pixel, the spectral resolution is about 0.001 98 nm/pixel, the total length is under 2.5 m. The telescope system′s effective area is calculated, and the telescope′s imaging quality and real field of view are given. The imaging quality of whole system, the smile and keystone of grating can satisfy the application demand.