Channel state information (CSI) plays a vital role in adaptive transmission systems, which adapt their transmission parameters to instantaneous channel conditions. However, the CSI tends to become outdated due to the rapid channel variation caused by multi-path fading. The inaccuracy of outdated CSI imposes a severe impact on the performance of a wide range of wireless systems, highlighting the significance of channel prediction that can combat the outdated CSI effectively. The aim of this paper is to propose a novel predictor, leveraging the strong time-series prediction capability of deep learning, where a deep recurrent neural network incorporating long short-term memory or gated recurrent unit is applied. Performance evaluation is carried out upon multi-antenna fading channels, and the numerical results in terms of prediction accuracy unveil that deep learning can bring a notable performance gain compared with the conventional predictors built on shallow neural networks.