The expressions of the Rayleigh range zR and turbulence distance zT of Gaussian-Shell model (GSM) beams propagating through non-Kolmogorov turbulence are derived, and the influence of turbulence parameters (generalized exponent parameter α、 inner scale l0and outer scale L0) on the spreading of partially coherent beams is studied. It is shown that zR decreases firstly and then increases due to increasing α. When α=3.11, zR reaches its minimum, which means that the spreading of beams is maximum. The Rayleigh range zR increases with decreasing outer scale L0 for 3.6<α<4 and increasing inner scale l0. When α>3.11, the influence of l0 on zR becomes smaller with larger α. It is worthy to be mentioned that the spreading of the beams is hardly affected by the turbulence within the Rayleigh range for small value of coherence parameter β or waist width w0, unrelated to α. Conversely, when the values of β or w0 are large enough, the spreading is affected by turbulence within Rayleigh range for different values of α. In addition, when the values of β or w0 are in a certain range, whether the spreading is affected by turbulence within Rayleigh range will be concerned with generalized exponent parameter α.