Based on extended Huygens-Fresnel principle, the average intensity and the beam width of Standard Laguerre Gaussian beams propagating in non-Kolmogorov turbulence were derived, making use of the Hermite polynomials. Numerical results show that the average intensity profile converts into Gaussian form more slower with larger beam orders and wavelength, or shorter propagating distance. Moreover, the beam width of Standard Laguerre Gauss beams is less affected by non Kolmogorov turbulence with larger turbulent power law exponent and inner scale, or smaller beam width of the fundamental Gaussian mode and outer scale of turbulence.