Mie-scattering lidar has been widely used in the detection of aerosol optical properties.However,this technology lacks accuracy in the determination of aerosol extinction coefficient boundary value and the logarithmic ratio of backscattering extinction.Based on the Klett backward integration model,a novel method for retrieving aerosol extinction coefficient is proposed.Firstly,by constructing a nonlinear equation,the boundary value of aerosol extinction coefficient is obtained by Steffensen iterative method.Secondly,the logarithm ratio of aerosol backscattering extinction is deduced by using differential absorption lidar function model.Finally,a feedback system is introduced to continuously correct the boundary value and reduce the error of the aerosol extinction coefficient inversion.The experimental results show that this algorithm can obtain the boundary value more quickly and invert the high-precision aerosol extinction coefficient,and the average relative error is less than 10 %,which should have broad application prospects in the aerosol detection.