In this paper a determination method for atmospheric aerosol extinction coefficient boundary value based on the fixed-point principle is proposed.The core idea of the method is to convert the determination of the atmospheric aerosol extinction coefficient boundary value to searching for the fixed point of function.Firstly,the relationships between the atmospheric extinction coefficient boundary value and the optical depth of atmosphere as well as the return signals of lidar are established.Secondly,the existence of fixed point is judged according to the existence and uniqueness condition of function′s fixed point,and then the atmospheric aerosol extinction coefficient boundary value is obtained by the fixed point iteration.The method is applied for real lidar return signals to invert the vertical profiles of lower atmospheric aerosol extinction coefficient,and it has been compared with the inversion results acquired by the clean layer method in the tropopause.The results show that the boundary value determined by this method can invert the lower atmospheric aerosol extinction coefficient well.This method can anticipate the existence interval of fixed point and select a reasonable initial iterative value.It has the advantages of fast convergence and few times of iterations.