Massive multiple-input multiple-output (MIMO) system is promising in providing unprecedentedly high data rate. To achieve its full potential, the transceiver needs complete channel state information (CSI) to perform transmit/receive precoding/combining. This requirement, however, is challenging in the practical systems due to the unavoidable processing and feedback delays, which oftentimes degrades the performance to a great extent, especially in the high mobility scenarios. In this paper, we develop a deep learning based channel prediction framework that proactively predicts the downlink channel state information based on the past observed channel sequence. In its core, the model adopts a 3-D convolutional neural network (CNN) based architecture to efficiently learn the temporal, spatial and frequency correlations of downlink channel samples, based on which accurate channel prediction can be performed. Simulation results highlight the potential of the developed learning model in extracting information and predicting future downlink channels directly from the observed past channel sequence, which significantly improves the performance compared to the sample-and-hold approach, and mitigates the impact of the dynamic communication environment.