Based on the extended HuygensFresnel principle and nonKolmogorov spectrum, analytical expressions for the beam width, angular spread and M2factor of HermiteGaussian (HG) beams through nonKolmogorov turbulence are derived. The results show that at a sufficiently long propagation distance(such as z≥3 km), the beam width, angular spread and the M2factor of HG beams through nonKolmogorov turbulence all increase with the increasing outer scale L0(3.6<α<4)and decreasing inner scale l0, and increase with the increasing exponent parameter α until it reaches its maximum value at α=3.11, then decrease with increasing α. However, the beam width and M2factor of HG beams hardly vary with increasing outer scale L0 in the region 3<α<3.6.