An approximately multi-user OFDM transceiver was introduced to reduce the multi-access interference (MAI ) due to the carrier frequency offset (CFO) to a negligible amount via precoding by Tsai, Lin and Kuo. In this work, we investigate the performance of this precoded multi-user (PMU) OFDM system in a time-variant channel environment. We analyze and compare the MAI effect caused by time-variant channels in the PMU-OFDM and the OFDMA systems. Generally speaking, the MAI effect consists of two parts. The first part is due to the loss of orthogonality among subchannels for all users while the second part is due to the CFO effect caused by the Doppler shift. Simulation results show that, although OFDMA outperforms the PMU-OFDM transceiver in a fast time-variant environment without CFO, PMU-OFDM outperforms OFDMA in a slow time-variant channel via the use of M/2 symmetric or anti-symmetric codewords of M Hadamard-Walsh codes.