The slit imaging spectrometer is one of the important tools for solar extreme ultraviolet (EUV) spectral imaging detection. However, at present, there is no such instrument load in China. The research of solar physics and space weather in the field of EUV spectral diagnosis mainly depends on foreign instrument data, which seriously restricts the development of related disciplines. The spectral imaging instruments that have been launched internationally have only a spatial resolution of 2'', and it is difficult to observe the core characteristics of the plasma related to the coronal heating mechanism predicted by the theoretical model. In order to better understand the coupling process between different layers of the sun’s atmosphere, solar physics research requires the observed data with wider spectral coverage. In light of this, we propose and design a sub-angular second spatially resolved solar extreme ultraviolet broadband imaging spectrometer operating in a band range of 62–80 nm and 92–110 nm. Compared with the existing instruments, the system can achieve high spatial resolution and spectral resolution, and wide spectral range coverage. Performance evaluation results indicate that the imaging spectrometer’s spatial resolutions in both bands are better than 0.4'', and their spectral resolutions are both better than 0.007 nm, with spectral imaging quality approaching the diffraction limit. The system designed in this work holds significant reference value for developing the first Chinese space-based solar EUV spectroscopic instrument in the future.