The millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems communicate at the extremely high-frequency band. In the extremely high band, the channel state information (CSI) from channel estimation will be outdated quickly, and herein, seriously degrading the system performance. In this paper, we focus on the channel prediction to obtain prior CSI in mmWave MIMO-OFDM systems. First, the mmWave MIMO-OFDM channel is categorized and represented in four domains: the array-frequency, array-time, angle-frequency, as well as angle-time. Then, for the above four domains, we investigate the effects of the channel representations on channel prediction, and analyze the mean-squared error performance as well as the computational complexity of the investigated prediction methods. We derive that the angle-time-domain prediction method achieves higher accuracy than the other three prediction techniques. In addition, we propose an enhanced angle-time-domain channel predictor by exploiting the spatial-time sparsity of the MIMO-OFDM channel to further improve the prediction accuracy. Finally, the simulation results confirm the statistical analysis and verify the superiority of the proposed predictors.