Based on the extended Huygens-Fresnel principle, the spreading of partially coherent cosh-Gaussian beams propagating through turbulent atmosphere is studied by using the incoherent superposition of higher-order Hermite-Gaussian beams. The analytic expression of the mean-squared width of partially coherent cosh-Gaussian beams in turbulence is derived. It is shown that the spreading increases with increasing turbulent parameter C2n and decentered parameter δ of the beams. However, partially coherent cosh-Gaussian beams with larger δ are less sensitive to the effect of turbulence than those with smaller δ.