The expression for the Rayleigh range of partially coherent annular beams propagating through non-Kolmogorov turbulence is derived, and the influence of turbulence parameters (generalized exponent parameterα , inner scale l0 , outer scale L0 ) and the beam parameters on the Rayleigh range is studied. It is shown thatRayleigh range zR| turb in turbulence decreases with increasing intensity of turbulence, and is always smaller than Rayleigh range zR| free in free space; zR| turb decreases with increasing L0 (just for 3.6 < α < 4 ) and increases with increasing l0 ; zR| turb does not monotonically vary with the increase of α , namely, it decreases firstly and then increases due to increasing α . When α = 3.11 , zR| turb reaches its minima. Additionally, the influence of turbulence on the Rayleigh range increases with increasing coherence parameter β , beam width w0 and decreasing obscure ratio ε , beam orders M(N ).