Abstract: Estimation of the wind velocity from weak aerosol backscattering signals is a key problem in the coherent wind lidar. The Cramer-Rao lower bound (CRLB) of the maximum likelihood (ML) discrete spectral peak (DSP) estimation is discussed based on the statistical model of the covariance matrix of zero mean complex Gaussian random process of the backscattering signal. The CRLBs of both the ML DSP and Fisher information matrix are compared. On the condition of the covariance matrix statistical model of the backscattering signals in coherent wind lidar, the performance of the ML DSP estimation is examined by employing the computer Monte Carlo simulations, and the probability density function of the estimations of the wind velocity is researched as well. The effects of signal-to-noise ratio, the accumulation number of the laser pulse as well as pulse width of the outgoing laser pulse on ML DSP wind velocity estimations are illustrated respectively. The calculation and simulation results show that, (1)The CRLB of the ML DSP estimation is lower than the exact CRLB from Fisher information matrix; (2)Both of the fractions of the bad estimations are 0, and the standard deviations of the good estimations are 0.62 m/s and 0.50 m/s, respectively, for SNR of －20 dB and 100 laser pulses accumulation and SNR of －30 dB and 10 000 laser pulses accumulation.