In this letter, we first investigate the bias of Doppler shift estimator based on autocorrelation function (ACF). Then we derive a signal-to-noise ratio (SNR) independent condition for Doppler shift estimation and achieve this condition by a adaptive process. Moreover, we present theoretical analysis about the convergency of our adaptive Doppler shift estimator, and derive a close-form expression for its mean square error (MSE). We verify the proposed estimator by computer simulation, the results of which are in agreement with the analysis, i.e., the proposed method achieves a good SNR-independent performance in a wide range of velocities and SNRs.