Orthogonal frequency-division multiplexing (OFDM) is a promising technology in broadband wireless communications, with its ability to transform a frequency-selective fading channel into multiple flat-fading channels. However, the time-varying characteristics of wireless channels induce the loss of orthogonality among OFDM subcarriers, which was generally considered harmful to system performance. In this paper, we propose a bit-interleaved time-frequency coded modulation (BITFCM) scheme for OFDM to achieve both the time and frequency diversity inherent in broadband time-varying channels. We will show that the time-varying characteristics of the channel are beneficial to system performance. Using the BITFCM scheme, and for relatively low maximum normalized Doppler frequency, a reduced-complexity maximum-likelihood decoding approach is proposed to achieve good performance with low complexity. For high maximum normalized Doppler frequency, the interearrier interference (ICI) can be large, and an error floor will be induced. To solve this problem, we propose two ICI-mitigation schemes by taking advantage of the second-order channel statistics and the complete channel information, respectively. It will be shown that both schemes can reduce the ICI significantly.