It is well-known now that orbital angular momentum (OAM) modes can be a potential technology to take full advantages of the space resources in the fiber-based optical communication system because of its infinite states. However, the corresponding fiber design for OAM modes to meet various requirements in the fiber-based communication system is still not enough. For the dispersion property, there are various attributes given in the standard of ITU-T series, which has not yet been proposed for the OAM modes. In this paper, we propose and design a non-zero dispersion-shifted air-core ring fiber for OAM mode, which can offer more options on dispersion values. A negative dispersion of −1.246 ps/(nm<inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>km) or a positive dispersion of 1.541 ps/(nm<inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>km) at 1550 nm with < 1.5 ps/(nm<inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>km) dispersion variation across the C band or < 4 ps/(nm<inline-formula> <tex-math notation="LaTeX">$\cdot $ </tex-math></inline-formula>km) dispersion variation across the C and L bands for OAM<inline-formula> <tex-math notation="LaTeX">$_{1,1}$ </tex-math></inline-formula> mode is achieved in the numerical simulation.