A novel frequency offset estimation technique based on maximum-likelihood estimation (MLE) for wireless OFDM communications over a doubly-selective fading channel is proposed. By taking advantage of subcarrier-level differential operation and coherent error characterization, the proposed estimator can effectively overcome frequency-selective fading effects. Frequency error characterization is achieved by pseudo-noise (PN) matched filters (MF) in the frequency direction; thus, the proposed estimation technique exploits frequency diversity with the maximum ratio combining (MRC). In addition, the proposed technique can combat the rapid time-selectivity caused by a wide Doppler spread because it requires channel stationarity for only a short duration due to the exploitation of both a single preamble in its training operation and the following semi-blind estimation aided from several pilot subchannels. The proposed technique can not only easily switch between training mode and semi-blind mode, but also easily swap from a coarse frequency offset estimation operation to a fine frequency offset estimation operation by sharing the same preamble block and the same system architecture. Extensive simulation results in conjunction with statistical analysis verify the superiority of the proposed technique.