Propagation of partially coherent cosh-Gaussian beam in non-Kolmogorov turbulence is studied theoretically. Based on extended Huygens-Fresnel principle, the averaged intensity and the power in the bucket of partially coherent cosh-Gaussian beam in non-Kolmogorov turbulence are derived. The influence of beam parameters and turbulence parameters is studied numerically. The investigation presents a reference for engineering applications, for example the remote sensing and the free-space communication.