Nonuniformly correlated partially coherent beams with radially symmetric coherence distributions, i.e., the radial partially coherent beams (RPCBs), can alleviate the scintillation induced by atmospheric turbulence and thus benefit the reception performance. We use wave optics simulation to study the propagation characteristics of coherent Gaussian beams, Gaussian Schell-mode beams, and RPCBs with convex Gaussian and super-Gaussian coherence distributions through anisotropic non-Kolmogorov turbulence. The effects of anisotropic parameters as well as non-Kolmogorov power spectrum index on far-field beam quality are analyzed in terms of far-field intensity profile and aperture-averaged scintillation index. The simulation results indicate that, the beam quality continues to deteriorate as the non-Kolmogorov spectrum index increases. On the other hand, the anisotropy will result in elliptical irradiance distribution in the far field. Therefore, instead of using a circular aperture with an equal-area elliptical aperture at the receiving end, the aperture-averaged scintillation index can be substantially reduced. Generally speaking, the propagation properties of RPCBs in anisotropic non-Kolmogorov turbulence remain superior to fully coherent beams as well as Gaussian Schell-model beams, especially for relatively small receiving apertures.