Abstract: Based on the Huygens-Fresnel principle, a closed-form propagation formula of anomalous vortex beams in atmospheric turbulence are derived.The influence of the atmospheric constant of refraction index structure and the beam size on the propagation characteristics are studied.The numerical simulations show that, in the same observation plane, the dark spot size of vortex beams decreases gradually and eventually disappear with the increase of refractive index structure constant.Furthermore, for the same atmospheric refraction rate, the dark spot size of the vortex beam decrease gradually with the increase of propagation distance.