We design a graded-index ring-core fiber with a GeO2-doped silica ring core and SiO2 cladding. This fiber structure can inhibit the effect of spin-orbit coupling to mitigate the power transfer among different modes and eventually enhance the orbital angular momentum (OAM) mode purity. By changing the high-index ring core from the step-index to parabolic graded-index profile, the purity of the OAM1,1 mode can be improved from 86.48% to 94.43%, up by 7.95%. The proposed fiber features a flexible structure, which can meet different requirements for mode order, effective mode area, etc. Simulation results illustrate that the parabolic-index ring-core fiber is promising in enhancing the OAM mode purity, which could potentially reduce the channel crosstalk in mode-division-multiplexed optical communication systems.