In the millimeter Linear FMCW radar system,the echo Doppler signal quadratic modulated by the target acceleration will cause the Doppler spectrum aberration and reduce the detection performance and parameter estimation precision.In this study,an optimal model based on the Maximum Likelihood(ML) method and its fast algorithm for velocity and acceleration estimation fitted for Gaussian noise were presented.Furthermore,the CRB of the parameter estimation of LFM under normal gauss circumstance was also derives.It provides the real low bounds for variance of estimated parameter.