The accurate prediction of the distribution load demand data is the corner stone of future planning of the power system networks and energy management strategies and policies. This paper presents a long short-term memory (LSTM) neural networks model to predict the distribution zone substation peak demand data in New South Wales state, Australia for 14 years and based on 15-minute intervals. The obtained results are compared with those obtained by feed-forward neural networks (FFNNs) and recurrent neural networks (RNNs) models. Three statistical performance evaluation, namely, the root-mean-square error (RMSE), mean bias error (MBE) and mean absolute percentage error (MAPE) are used to verify the effectiveness of the proposed model. The RMSE, MBE and MAPE of the LSTM neural network model are 1.2556%, 1.2201% and 2.2250%, respectively. In addition, the computational time is 12.3309 second which is faster than FFNNs and RNNs models. The results show the effectiveness of the proposed model over the aforementioned models in terms of accuracy and computational speed.