In order to overcome the frequency offset existing in short-wave （ namely high-frequency ， HF ） burst-mode communication ， an iterative frequency offset estimation algorithm on the basis of interpolation using Fourier coefficients is proposed ， which takes into consideration the waveform of HF modem under low signal-to-noise ratio （SNR）.Theproposedestimatoristackledinseveralstages.Firstly ， acoarseestimationofpeakfrequencyismade bythe application ofdiscrete Fourier transform （ DFT ） . Secondly ， Jacobsen ’ s method is used to interpolate DFT sam-ples ， and a bias analysis of the interpolating results is carried out. Then ， variance as a function of SNR and training sequence length is obtained ， and a confidence interval with a confidence coefficient of 0.99999 ， which is used as the searching interval of frequency offset estimation ， is adaptively adjusted. Finally ， a combination of parabolic interpolation is made with the iterative method to obtain an accurate result through the interval.Simulated results show that the proposed algorithm helps achieve Cramer-Rao low bound （ CRLB ） at low SNR with the training sequences equal to 128 ， 256 and 512. Especially ， at 0dB ， the estimator ’ s mean square error is about 1.005 times that of CRLB only with two iterations.