We propose a new fine Doppler frequency estimator using two fast Fourier transform (FFT) samples for pulse Doppler radar that offers highly sensitive detection and a high resolution of velocity. The procedure of fine Doppler frequency estimation is completed through coarse frequency estimation (CFE) and fine frequency estimation (FFE) steps. During the CFE step, the integer part of the Doppler frequency is obtained by processing the FFT, after which, during the FFE step, the fractional part is estimated using the relationship between the FFT peak and its nearest resultant value. Our simulation results show that the proposed estimator has better accuracy than Candan's estimator in terms of bias. The root mean square error (RMSE) of the proposed estimator has more than 1.4 time better accuracy than Candan's estimator under a 1,024-point FFT and a signal-to-noise ratio (SNR) of 10dB. In addition, when the FFT size is increased from 512 to 2,048, the RMSE characteristics of the proposed estimator improve by more than two-fold.