An imaging spectrometer with a varied line-space convex grating was designed and optimized in this study to realize a large relative aperture, high-resolution imaging, and light miniaturization, thus ensuring easy processing, assembly, and adjustment of the optical system based on a simple system structure. With a double-element system in a reflection concentric structure, the complexity and application limitations of the existing aberration-correction configurations were overcome. An aberration-correction design method was proposed based on the aberration theory of gratings, and a theoretical model of the geometric aberration of the system was briefly derived. The focal conditions of the system in both the meridional and sagittal directions were then analyzed in combination with the Rowland circles of the concentric configuration.This analysis established a mathematical model of the relationship between the astigmatism and line spacing of the convex grating. Finally, an anastigmatic design of the imaging spectrometer with a convex grating was realized using a global optimization algorithm. Design results show that the system can achieve high-quality imaging in the spectral range of 300~800 nm with a large relative aperture of F/2.7 and a resolution of 1.9 nm.In addition, approximately 201 hyperspectral channels are covered. The modulation transfer function for the whole spectral band is greater than 0.7, which meets the design requirements of the system. This study contributes significantly to the research of hyperspectral imaging spectrometers with aberration-correction convex gratings in terms of light weight and compactification.