This paper proposes a new technique for frequency offset correction for OFDM systems on a frequency selective fading channel. Frequency offset in OFDM introduces interchannel interference among the multiple subcarriers of OFDM signal. To compensate the interference, this paper describes an algorithm with two stages:acquisition and tracking. At both stages, the proposed algorithm oversamples the received OFDM signal to obtain a couple of demodulated symbol sets. At acquisition stage the frequency offset is reduced to half or less of the intercarrier spacings by matching the sign pattern of each element of the sets. Next, at tracking stage the frequency offset is corrected with a frequency detector which is controlled by the correlation of the two sets. It is shown that the proposed algorithm can correct the frequency offset in the event of uncertainty in the initial offset that exceeds one half of the intercarrier spacing. In addition, the proposed algorithm is robust to transmitted symbols and channel characteristics by using oversampled symbol sets.