Many bit and power allocation algorithms have been recently developed for OFDM systems assuming perfect knowledge of the channel state information (CSI). In practice, however, these algorithms experience significant performance loss due to the inaccuracies in CSI. For time-varying channels the imperfect channel state information due to outdated channel estimates is a major source of these inaccuracies. To mitigate this effect, we propose to predict the channel state information and devise the bit and power allocation algorithm using the predicted CSI. We study several channel prediction algorithms for OFDM systems and present robust bit and power allocation schemes based on the predicted CSI. Simulation results show that for Doppler frequencies up to 100Hz, the proposed bit and power allocation algorithms (using the predicted CSI) can achieve performance close to that of the algorithms that assume perfect knowledge of CSI.