The UAV industry has developed rapidly in recent years, and has broad application prospects in both military and civilian applications. The track record of UAV plays an important role in its navigation process, and the track prediction of the UAV has also become a hot spot in the current world research. The use of neural network for track prediction can develop to its advantages. Firstly, the domestic and foreign scholars' literatures on track prediction are sorted out, and the current aircraft track prediction algorithms are summarized and classified according to the principle of track prediction. The problem of improving prediction accuracy is studied. Then, aiming at the problem that the prediction accuracy of the traditional neural network model is not high enough, an error-corrected nested long short-term memory (ENLSTM) neural network prediction model is proposed. ENLSTM introduces an error correction term based on the nested long short-term memory network model, which makes the prediction accuracy higher. Finally, four neural network models of BP, RNN, LSTM and ENLSTM are used to simulate the real track data and simulated track data of the UAV respectively. It is concluded that RNN has more advantages in the prediction of UAV track than BP neural network. The gradual improvement based on the basic RNN model improves the prediction ability of the model. ENLSTM model has a better effect on the track prediction of UAV.