To study the regions of spreading of truncated beams propagating through non-Kolmogorov turbulence, the expressions for turbulence distance and Rayleigh range are derived, the transport path is divided into three regions, and the relevant numerical analysis of the three regions is given. Results show that the lengths of the first region and the second region decreases with increase of coherence and truncation parameter, and the starting point of the third region reduces with increase of coherence and truncation parameter. The smaller coherence and truncation parameter are, the more likely it is to ignore the effect of turbulence on the beam propagation in Rayleigh range. In the three regions, the turbulent distance increases with the change of the generalized exponential. The corresponding physical explanations are given for the main results.