In order to solve the problem of the contradiction between capturing range and estimation accuracy of frequency offset estimation methods for low signal to noise ration(SNR) condition,an new carrier frequency offset estimation algorithm based on FFT and long delay autocorrelation function is proposed.The new algorithm uses estimated frequency offset obtained by FFT to adjust frequency offset,so the remainder frequency offset is in the range of frequency offset that the long delay autocorrelation function can handle.Accurate frequency offset estimation is obtained by calculating the weighted sum of the rough estimation which is obtained from several long delay autocorrelation function.It extends its estimation range to a half data rate,at the meantime,its SNR threshold is low at small SNR,the frequency estimation capacity in the whole frequency range is steady.The simulations illustrate the algorithm performance of high estimation accuracy,wide capturing range and steady capacity.