Abstract: To study the spreading of cosh-Gaussian beams propagating through non-Kolmogorov turbulence, extended Huygens-Fresnel principle was used. The expression of turbulence distance zt of partially coherent cosh-Gaussian beams propagating through turbulence was derived. The influence of turbulence parameters (generalized exponent parameter , inner scale l0 and outer scale L0) and beam parameters (coherence parameter and decentered parameter )on turbulence distance was studied theoretically. The results show that turbulence distance zt decreases firstly and then increases with the increase of . When =3.11, zt is minimum. And zt increases with the increase of l0 and , decreases with the increase of L0(just for 3.64) and . The results will be useful for the applications of cosh-Gaussian beams propagating in non-Kolmogorov turbulence.