Convex grating is the core of Offner structure imaging spectrometers. To improve the imaging quality of a spectrometer and realize remote sensing detection, it is key to use convex grating with high diffraction efficiency and high resolution. The diffraction efficiency of convex gratings is analysed by strictly coupled wave theory. In this study, we present the research status of convex grating and discuss the main methods for designing and manufacturing convex blazed grating, including electron beam direct writing, X-ray lithography, mechanical etching, and holographic ion beam etching. Owing to the advantages of holographic ion beam etching, such as low cost, controllable groove type, and ghost-free, we introduce in detail the fabrication of convex grating via holographic ion beam etching and present related studies. Based on the investigation and analysis, we aim to optimize and improve the uniformity of the light intensity distribution of holographic exposure, the adjustable rotation axis of swing-etching device, and the process parameters of ion beam etching to produce a practical convex-blazed grating.