The thesis deals with frequency offset estimation method in time-varying channels that vary within the training sequence. As carrier frequency and mobile speed increase in the systems beyond IMT-2000, channels vary within the training sequence. When the training sequence duration is less than 10% of the channel coherence time, time-varying channels can be assumed to vary in a linear fashion. Under this assumption, the signal model in time-varying channels can be modified by using linear interpolation between first channel information and last channel information. Then, a frequency offset and channels can be jointly estimated by maximum likelihood (ML) estimator. Besides, the orthogonal frequency division multiplexing (OFDM) systems are sensitive to the frequency offset and the proposed frequency offset estimator is applied to OFDM systems based on the systems beyond IMT-2000. It is shown by computer simulations that the proposed method improves mean square error (MSE) performance under the given environments.