Abstract: An extreme ultraviolet solar corona multispectral imager can allow direct observation of high temperature coronal plasma, which is related to solar flares, coronal mass ejections and other significant coronal activities. This manuscript proposes a novel end-to-end computational design method for an extreme ultraviolet (EUV) solar corona multispectral imager operating at wavelengths near 100 nm, including a stray light suppression design and computational image recovery. To suppress the strong stray light from the solar disk, an outer opto-mechanical structure is designed to protect the imaging component of the system. Considering the low reflectivity (less than 70%) and strong-scattering (roughness) of existing extreme ultraviolet optical elements, the imaging component comprises only a primary mirror and a curved grating. A Lyot aperture is used to further suppress any residual stray light. Finally, a deep learning computational imaging method is used to correct the individual multi-wavelength images from the original recorded multi-slit data. In results and data, this can achieve a far-field angular resolution below 7", and spectral resolution below 0.05 nm. The field of view is ±3 R_☉ along the multi-slit moving direction, where R_☉ represents the radius of the solar disk. The ratio of the corona's stray light intensity to the solar center's irradiation intensity is less than 10⁻⁶ at the circle of 1.3 R_☉.