Based on the extended Huygens-Fresnel principle, the definition of second-order moments of the Wigner distribution function (WDF), and the non-Kolmogorov turbulence spectrum, analytical expressions for the M 2 -factor and Rayleigh range of correlated combination partially coherent Hermite-Gaussian linear array (PCHGLA) beams propagating through non-Kolmogorov turbulence have been derived. The effect of non-Kolmogorov turbulence and array beam parameters on the M 2 -factor and Rayleigh range is discussed in detail. The results show that the M 2 -factor and Rayleigh range, as well as their corresponding relative quantities of the PCHGLA beams, vary non-monotonically with increasing generalized exponent parameter α of the turbulence, and M 2 -factor exists a maximum whereas Rayleigh range exists a minimum at α = 3.11, respectively. The M 2 -factor and Rayleigh range of PCHGLA beams increase with increasing beam number but oscillate with increasing relative beam separation distance x 0 0 for x 0 0 < 1 and then increase monotonically as x 0 0 increases for x 0 0 > 1. The PCHGLA beams are less affected than the GSM linear array beam under the same conditions.