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This paper introduces a novel channel-prediction technique for an orthogonal frequency-division multiplexing (OFDM)/frequency-division duplex (FDD) system to support an adaptive-modulation and coding (AMC) scheme over a rapidly time-varying multipath fading channel. Most channel-prediction techniques assume that there is no channel variation in the predefined time duration, e.g. the slot. As a result, those techniques cannot compensate for the degradation of packet-error-rate (PER) performance, resulting from the rapid channel variation over the slot duration. In this paper, we propose a novel two-step channel-prediction technique that considers the time-varying nature of a channel over the duration of interest. Simulation results show that the AMC scheme of the OFDM/FDD system utilizing the proposed channel-prediction technique can guarantee the target PER of 1% without any loss of system throughput compared with a case supported by a conventional channel prediction under ITU-R Veh A 30 km/h.