Forecasting energy data, especially the primary energy requirement, is the key part of policy-making. For those territories of different developing types, seeking a knowledge-based and dependable forecasting model is an essential prerequisite for the prosperous development of policy-making. In this paper, both autoregressive integrated moving average and backpropagation neural network models which have been proved to be very efficient in forecasting are applied to the forecasts of the primary energy consumption of three different developing types of territories. It is shown that the average relative errors between the actual data and simulated value are from 4.5% to 5.9% by the autoregressive integrated moving average and from 0.04% to 0.47% by the backpropagation neural network. Specially, this research shows that the backpropagation neural network model presents a better prediction of primary energy requirement when considering gross domestic product, population, and the particular values as predictors. Furthermore, we indicate that the single-input backpropagation neural network model can still work when the particular values have contributed most to the energy consumption.