A swing ion-beam etching method to fabricate convex blazed gratings used in shortwave infrared hyperspectral imaging spectrometers is presented. This method solves the consistency problem of blaze angles by swing etching through the meridian direction of the gratings. The mathematical relationship of the curvature, aperture, and diffraction efficiency of convex gratings is studied to demonstrate the limitation of conventional translational lithography and the necessity of swing etching. A geometric model is built to analyze the influence of swinging speed and beam slit width on groove evolution. Convex gratings with a 45.5 gr/mm groove density, 67 mm aperture, 156.88 mm radius of curvature, and 2.2° blaze angle have been fabricated and measured where the peak and average diffraction efficiency in the shortwave infrared band reach 90% and 70%, respectively. Experimental results validate that high-efficiency convex gratings of small blaze angle and high groove consistency can be produced by swing etching, which satisfy the requirements for high spectral resolution and miniaturization of imaging spectrometers.