Extended Huygens-Fresnel principle is used to analyze the optical intensity transverse distribution of higher-order Bessel Gaussian beam (BGB) propagation through non-Kolmogorov (NoK) atmosphere turbulence model. In NoK turbulence model, the distance and power law effect the strength of phase perturbed by turbulence. So the result by numerical integral shows that the intensity distribution of BGB beam gets more severe changes at large distance. The higher order beam is less effected by turbulence than lower order beam. The lager transverse parameter of the source can get more spreads when it propagates through turbulence.