Optical fiber is an important transmission medium in optical communication system. We have designed circular step index fiber and circular graded-index fiber for Orbital Angular Momentum (OAM) transmission. And we calculate the existing vectormodes in fiber through the software COMSOL Multiphysics. The step-index fiber has a high refractive index ring which doped with Pb S quantum dots between the core and the cladding. And the refractive index difference between the ring and the cladding reaches 0.035, which weaken the degeneracy of adjacent eigenmodes. Numerical analyses show the step-index ring core fiber can support the long-distance transmission for the OAM mode of 11,1=1,5,6,7 in the wavelength range of 1530nm to 1565nm (11,1 refers to the mode order of orbital angular momentum, called topological charge). In order to enhance its stability, we adjust the ring to be a graded refractive index profile, which increases the effective refractive index difference between the vector modes from the same mode order. This fiber design not only increases transmission stability, but also has a better manufacturing process than the step-index fiber. From the simulation results, we can fmd that the graded-index fiber with a gradation rate alpha =8 provides a relatively large effective refractive difference. The effective refractive difference is 1.68 x 10(-4) , 1.42 x 10(-4) and 2.44 x 10(-4) respectively corresponding to L=1, 5, and 6 at a wavelength of 1550 nrn While the effective refractive index difference is 1.65 x 10(-4) , 0.9 x 10(-4) and 1.52 x 10(-4) for the step-index optical fiber.