Natural gas consumption is an important indicator of energy utilization and demand, and its scientific and high-accuracy prediction plays a key role in energy policy formulation. With the development of deep neural networks and ensemble learning, a homoheterogeneous stacking ensemble learning method is proposed for natural gas consumption forecasting. Firstly, to obtain the potential data characteristics, a nonlinear concave and convex transformation-based data dimension enhancement method is designed. Then, with the aid of a stacking ensemble learning framework, the multiscale autoregressive integrated moving average (ARIMA) and high-order fuzzy cognitive map (HFCM) methods are chosen as the base learner models, while the meta learner model is constructed via a well-designed deep neural network with long short-term memory (LSTM) cells. Finally, with the natural gas energy consumption data of national and 30 provinces (where the data of Xizang are unavailable) of China from 2000 to 2019, the numerical results show the proposed algorithm has a better forecasting performance in accuracy, robustness to noise, and sensitivity to data variations than the seven compared traditional and ensemble methods, and the corresponding model applicability rate could achieve more than 90%.