The low-frequency and mmWave links usually co-exist in the next generation wireless terminals, where the low-frequency link is always on and the mmWave link becomes active when high rate transmission is required. Since low-frequency and mmWave channels have spatial similarities, it is feasible to utilize low-frequency channel information to reduce the beam training overhead in mmWave communications. In this paper, we propose a deep learning assisted beam prediction scheme using out-of-band information extracted from low-frequency channel state information (CSI). To overcome the inaccuracy in estimating spatial features due to small number of antennas in low-frequency band, deep learning is introduced to extract robust channel features and increase the prediction accuracy. Moreover, dedicated pre-processing algorithm and network architecture are derived to improve the performance. Simulation results demonstrate that the proposed scheme is robust to various CSI matrix sizes and signal-to-noise ratio. By exploiting low-frequency CSI, it could successfully predict the optimal beam direction to facilitate the initial beam training in mmWave communications with over 94% accuracy in line-of-sight scenarios, which can reduce the overhead of beam training significantly.