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In a time-varying mobile channel, the Doppler effect causes intercarrier interference (ICI) in an OFDM system. Some researches have been found to mitigate the ICI effect in order to improve the system performance. However, ICI reduction algorithms usually require the information of the channel impulse response (CIR) even on each sample. In this paper we study several channel estimation algorithms for CIR estimation, including the frequency-domain and the time-domain approaches. We have shown that the time-domain Kalman filter channel estimator has better performance than others because it can estimate CIR sample by sample Simulation results also show that a proposed ICI mitigation algorithm incorporating the time-domain Kalman channel estimator achieves better BER performances at different mobile speeds.