Considering the influence of acceleration and the Gaussian envelope on laser Doppler velocimeter (LDV), the parameters estimation of Doppler signal with Gaussian envelope is investigated based on introducing the acceleration. According to the theory of mathematics statistics, the Cramer-Rao lower bounds (CRLB) of Doppler circular frequency and its first order rate of change are analyzed, formulas of CRLB are given, and the power spectrum estimation with adjustment is discussed. The theoretical analysis and simulation results show that the CRLB of the variance of estimated parameters are related to the observation data, signal-to-noise ratio (SNR), the width of Gaussian envelope, and it can be decreased by increasing the length of observation data and improving the SNR. When the length of observation data is fixed, the larger the acceleration is, the narrower the Gaussian envelope is, and the CRLB of Doppler circular frequency and its first order rate are also larger. The gap between the variances of the measuring results and the CRLB narrows when the SNR of the signal is improved, almost eliminates when the SNR is higher than 6 dB. The acquired result is in harmony with those acquired by other researchers.