Based on the extended Huygens-Fresnel principle, the expression for the turbulence distance of partially coherent cosh-Gaussian (ChG) array beams propagating through atmospheric turbulence is derived by using the quadratic approximation of Rytov′s phase structure function and the integral transform technique. It is showed that the turbulence distance depends on the atmospheric turbulence intensity, the beam parameters (i.e., the beam number, the beam coherence parameter, the decentered parameter, the relative separation distance of beams), the type of the beam superposition (i.e., the superposition of the cross-spectral density function and the superposition of the intensity) and so on. It is also showed that the turbulence distance of the partially coherent ChG array beams will increase with the atmospheric turbulence intensity, but the effect of turbulence on the spreading of partially coherent ChG array beams can be reduced by choosing the suitable beam parameters and the suitable type of the beam superposition.