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One of the well known problems in an orthogonal frequency division multiplexing (OFDM) system is its vulnerability to frequency offset. In practice, most coherent OFDM systems transmit pilot symbols on some of the subcarriers to estimate channel attenuation and also add a cyclic prefix (CP) to avoid intercarrier interference and intersymbol interference. A hybrid maximum likelihood estimation algorithm based on the redundancy of both cyclic prefix and pilot subcarriers is proposed for the correction of frequency offset. If the frame timing has been synchronised in advance, by considering the two kinds of redundancy simultaneously, the performance of the proposed hybrid algorithm could achieve significant improvement under low SNR and short CP. As to high SNR and long CP, the performance of this hybrid algorithm is almost identical to that of CP-based only algorithm. Some comparative simulations are given to illustrate the advantages of the proposed hybrid estimation scheme.