The influences of turbulent atmosphere on the Rayleigh range are studied by analytical and numerical calculation with Andrews modified fluctuation spectrum (or M spectrum) when coherent cosh-Gaussian beams transfer both in free space and in atmospheric turbulence.The results show that the Rayleigh ranges in turbulent atmosphere are less than that in free space.The Rayleigh range ZR increases with the increase of the beam coherence parameter α,the beam parameter β,the inner size of atmospheric turbulence l0 and the Gaussian waist width ω0,while decreases with the increase of the wave length λ and the turbulent strength C2n.It is also showed that the Rayleigh range ZR is affected significantly by the inner size of atmospheric turbulence l0 while it is affected little by the outer size of atmospheric turbulence L0,hence the size effect appears.The results are consistent with what is derived with the Von Karman fluctuation spectrum under the same condition.