We simulate and analyze the mode properties and propagation effects of orbital angular momentum (OAM) modes in a ring fiber. A ring fiber with 0.05 up-doping is designed in simulation to support up to 10 OAM modes while maintaining single-mode condition radially. With a multiple-ring fiber, tens of OAM modes can be potentially multiplexed to greatly enhance the system capacity and spectral efficiency. The mode index difference can be maintained above 10^-4 over hundreds of nanometers optical bandwidth. Higher order OAM modes' azimuthal intensity and odd-order OAM modes' azimuthal phase show better tolerance to the fiber ellipticity. Moreover, higher order OAM modes also have longer 2π and 10-ps walk-off length. After 600-km propagation, OAM_0,4 mode shows <; 10-ps mode walk- off, even in a ring fiber with 1% ellipticity. Also, in such an elliptical fiber, the well-aligned OAM modes with different charges have <;-20 dB intermode crosstalk. The improvement of the circularity for the ring fiber is expected to reduce the crosstalk and increase the demultiplexing efficiency.