A novel predictive dynamic bandwidth allocation (DBA) method based on the long short-term memory (LSTM) neural network is proposed for a 10-gigabit-capable passive optical network in mobile front-haul (MFH) links. By predicting the number of packets that arrive at the optical network unit buffer based on LSTM, the round-trip time delay in traditional DBAs can be eliminated to meet the strict latency requirement for MFH links. Our study shows that the LSTM neural network has better performance than feed-forward neural networks. Based on extensive simulations, the proposed scheme is found to be able to achieve the latency requirement for MFH and outperforms the traditional DBAs in terms of delay, jitter, and packet loss ratio.