Frequency offset estimation is an important technique in receiver design of wireless communications. In many applications, sampled single frequency tone is selected as training symbol/sequence for frequency synchronization. Under this assumption, frequency offset estimation can be regarded as the problem of single carrier frequency offset estimation. In this Letter, an approximate maximum likelihood frequency estimator is proposed. This estimator is efficient at moderate and high SNR's. Compared with other estimators, the proposed estimator is less sensitive to the variance threshold and offers feasible levels of computation complexity. The proposed estimator is suitable for high frequency offset cases and coarse/fine frequency synchronization applications.