In order to analyse the influence of atmospheric turbulence on the pro pagation intensity of hollow vortex beams,based on the extended Huygens-Fresne l principle and the approximation of Rytov phase structure function,the analytic al expression of propagation intensity for Hollow Gaussian vortex (HGV) beams th rough anisotropic non-Kolmogorov turbulence is derived by using anisotropic non - Kolmogorov turbulence spectrum model.By numerical simulation,the effects of pr opagation distance,turbulence parameters and beam parameters on the intensity d istribution are analysed.The results indicate that the intensity of the HGV bea ms will gradually evolve from hollow to Gaussian distribution with the increasin g propagation distance,and the larger topological charge,the smaller waist wid th and the longer wavelength,the smaller the intensity evolution of the HGV bea ms is affected by anisotropic atmospheric turbulence.When the larger anisotropi c turbulence coefficient,generalized exponent factor and inner scale are,and t he smaller turbulence outer scale and structure constant are,the intensity evol ution of the HGV beams will slow down with the increasing propagation distance, which indicates that the propagation intensity distribution of the HGV beams in the weaker anisotropic non-Kolmogorov atmospheric turbulence is less affected b y the turbulence.