One of the major difficulties in realizing a high-dimensional frequency converter for conventional optical vortex (COV) modes stems from the difference in ring diameter of the COV modes with different topological charge numbers l. Here, we implement a high-dimensional frequency converter for perfect optical vortex (POV) modes with invariant sizes by way of the four-wave mixing (FWM) process using Bessel–Gaussian beams instead of Laguerre–Gaussian beams. The measured conversion efficiency from 1530 to 795 nm is independent of l at least in subspace l∈{-6,…,6}, and the achieved conversion fidelities for two-dimensional (2D) superposed POV states exceed 97%. We further realize the frequency conversion of 3D, 5D, and 7D superposition states with fidelities as high as 96.70%, 89.16%, and 88.68%, respectively. The proposed scheme is implemented in hot atomic vapor. It is also compatible with the cold atomic system and may find applications in high-capacity and long-distance quantum communication.