Based on the non-Kolmogorov spectrum and the generalized Huygens-Fresnel principle, taking the cosh-Gaussian (ChG) vortex beams as a typical example, the distance for the conservation of topological charge of partially coherent ChG vortex beams propagating through non-Kolmogorov atmospheric turbulence is studied. With the increment of general structure constant C～2n and the waist width w0, as well as the decrement of the general exponent α, the inner scale l0 and spatial correlation length σ0, the distance for the conservation of topological charge will decrease , whereas outer scale L0 and part parameters of hyperbolic cosine Ω0 has no effect on the distance for the conservation of topological charge.