In this work, we design and simulate an air-core As2S3 ring fiber for high-order orbital angular momentum (OAM) supercontinuum generation. We show that the chromatic dispersion of the ring fiber can be substantially tailored by proper optimization of the air-core radius. Two-octave supercontinuum carrying OAM17,1 mode, spanning from 1560 to 6250 nm, is obtained by pumping a 50-fs 100-kW secant hyperbolic pulse centered at the wavelength of 3800 nm into the designed fiber with 50-μm air-core radius and 1-μm ring width. We further engineer the chromatic dispersion of some other OAM modes and perform simulations of supercontinuum spectra using different kilowatt-level peak power, which indicates that the fiber we design represents a promising avenue for supercontinuum generation of all the OAMl,1 modes (|l| ≤17). The proposed fiber is suitable for the transmission of OAM beams in infrared wavelength range and it could promote the development and application of high-order OAM beams.