Multi-carrier code division multiple access (MC-CDMA) has been considered as one of the promising techniques for the next generation of mobile communication systems because of its efficient bandwidth usage, robustness to the multi-path fading and simple channel-sharing scheme. However, MC-CDMA cannot be employed in the uplink communication where the transmitted signal from each user propagates through the different multi-path fading channel, and the received signals are no longer orthogonal at the base station. As a result, bit error rate (BER) performance in the uplink MC-CDMA communication would be strongly degraded due to the occurrence of multi-user interference (MUI). To solve the MUI problem in the uplink MC-CDMA, the pre-equalization method was proposed in which the uplink signal is pre-equalized at the user terminal by using the channel response estimated from the downlink. Although the pre-equalization method is very effective for the stationary uplink channel with fixed users, it is hard to be employed in the time varying fading channel with mobile users, because there is a big difference in the channel responses between downlink and uplink. For the efficient MUI compensation, each user terminal would be required to predict the future channel conditions based on the current observation. This paper proposes a method for model based uplink channel response prediction by employing the spectral decomposition of the downlink channel impulse response. Computer simulation results show that the proposed method can achieve the accurate prediction of channel response for mobile users during the uplink transmission and allows the effective MUI compensation.