As an efficient, economical, and clean energy, natural gas plays an important role in the development of the new energy revolution. Accurate prediction of natural gas consumption and production can adjust energy deployment in advance, which can ensure the stable operation of natural gas. Considering the complex and non-linear characteristics of natural gas production and consumption data, this paper develops a new hybrid forecasting model (WPD-VMD-LSTM) based on the fuzzy entropy, variational mode decomposition (VMD), wavelet packet decomposition (WPD), and Long Short-Term Memory (LSTM). In this model, WPD and VMD undertake the tasks of primary and secondary decompositions, respectively; fuzzy entropy is used for the preprocessing process before the re-decomposition; and LSTM is used to predict the decomposed time series. In particular, the different criteria set by fuzzy entropy lead to the establishment of two prediction models. Then, two models are used to study monthly natural gas consumption and production in the USA. The results demonstrate that the proposed model performs significantly better than other comparable models and the target model has some practical value. Meanwhile, models may cope with different types of energy data, and models can accurately predict energy transformations with strong applicability, which can be applied to future energy forecasting in various fields. Finally, the constructed models are used to forecast the NGC and NGP in the USA in the next 3 years and make reasonable policy recommendations based on the forecast results.