In recent years, massive multiple-input multiple-output (MIMO) has been regarded as a promising technique in the fifth-generation (5G) communication systems. With the ability of focusing transmission beams on users, massive MIMO has a natural advantage in the field of physical layer security to improve the system secrecy performance. However, in practical mobile systems, the imperfect channel state information (CSI) caused by the channel estimation error and the transmission and processing delay will have a non-negligible impact on the system performance. In this paper, we investigate secure communications in a multi-user massive MIMO-enabled vehicular communication networks. Considering the influence of imperfect CSI on the secrecy performance, we derive a tight asymptotic lower bound of the system secrecy capacity under both perfect and imperfect CSI. Moreover, we further analyze the impact of vehicle speed on the system secrecy performance and propose a channel prediction scheme based on (Long Short-Term Memory) LSTM model to compensate for the negative effects of imperfect CSI, which can improve the system secrecy performance in high mobility scenario. Simulation results show that the imperfect CSI severely reduces the system secrecy capacity, but its negative effects can be effectively alleviated through the designed LSTM-based channel prediction and compensation scheme.