Quantitative evaluation of phase disto rtion of Laguerre-Gauss (LG) beams which propagate in a turbulence atmosphere h as a significance guidance effect on compensation and enhancement of the quality of the free space optical communication based on orbital angular momentum (OAM).The root mean square (RMS) based on Zernike polynomials is proposed as an impor tant figure to evaluate the wavefront aberration,and the atmospheric turbulence is simulated by a random ph ase screen using the method of sub-harmonics (SH).Using Matlab,RMSs of phase distortions of LG beams with various topological charges are investigated and analyzed.It is found that the random phase screen simulated by sub-harmonics method is more cl ose to the actual atmospheric turbulence than that simulated by the Fourier transfor m(FFT) method.In addition,the atmospheric turbulence has a strong effect on the transmission properties of LG beams,and the phase distribution of LG beams suffers dama ge related to the OAM values (topological charge value) and the transmission di stance. Moreover,the calculation results of the RMSs of LG beams show the same regularity with the simulation results of the phase distortions.As an example,when the transmission distance is 500m,the RMS values of the wav e front distortion of LG beams with the OAM values l＝1,l＝3,l＝5and ar e 0.0040,0.0049and 0.0059,which shows that the wavefront distortion is more serious.When the OAM value is l=1and the transmission distance is extended from 500m to 4500m,the wa vefront distortion is also increased with the increase of RMS from 0.0040to 0.0058.Consequently,the RMS can reflect the wavefront distortion accurately and objectively.