Based on the extended Huygens-Fresnel principle and the method of second moments of the Wigner distribution function, the analytical formulas for the root-mean-square (RMS) spatial width, the RMS angular width, and the M2-factor of the partially coherent cosh-Gaussian (ChG) beam in turbulent atmosphere have been derived, which can be applied to cases of different spatial power spectra of the refractive index fluctuations of the turbulent atmosphere. It can be shown that the RMS angular width, M2 factor and relative M2 factor of a partially coherent ChG beam in turbulence increase with the propagation distance and depend on the waist width, wavelength, coherent parameter, decentered parameter, and spatial power spectrum of the refractive index fluctuations. The RMS angular width as a function of the decentered parameter has a minimum at any given propagation distance. For long propagation distance, the M2-factor as a function of the decentered parameter also has a minimum, and the beams with a larger decentered parameter are less affected by the turbulence.