Considering the influence of acceleration and the Gaussian envelope for a laser Doppler velocimeter (LDV), parameter estimation of a Doppler signal with a Gaussian envelope was investigated based on introducing acceleration. According to the theory of mathematics statistics, the Cramer–Rao lower bounds (CRLBs) of Doppler circular frequency and its first order rate were analyzed, formulas of CRLBs were given, and the power spectrum estimation with adjustment was discussed. The results of theory and the simulation show that the CRLBs are related to the data length, the signal-to-noise ratio (SNR), and the width of the Gaussian envelope, and they can be decreased by increasing the data length or improving the SNR; the larger the acceleration is and the narrower the Gaussian envelope is, the larger the CRLBs of Doppler circular frequency and its first order rate are; the gap between the variances of the measuring results and the CRLBs narrows when the SNR of the signal is improved, and is almost eliminated when the SNR is higher than $6\mathrm{dB}$ . It is concluded that the model presented is much more suitable for a LDV than that acquired by Rife and Boorstyn [IEEE Trans. Inform. Theory 20, 591 (1974)].