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 arcsec, 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 observation data with wider spectral coverage. In light of this, we propose and design a sub-angular second spatial resolved solar extreme ultraviolet broadband imaging spectrometer operating in the 62~80nm and 92~110nm bands. Compared with the existing instruments, the system can achieve higher spatial and spectral resolution and wider spectral range coverage. Performance evaluation results indicate that the imaging spectrometer's spatial resolution in both bands is better than 0.4 arcsec, and the spectral resolution is better than 0.007nm, with spectral imaging quality approaching the diffraction limit. The system designed in this paper holds significant reference value for the development and research of China's first space-based solar EUV spectroscopic instrument in the future.