Due to the various ecological environment, economic development and resources, the main influencing factors of natural gas consumption are different in the eastern, central and western areas of China. To fully understand such discrepancy, we adopted the grey relation analysis (GRA) to select three main significant factors from 7 potential impacts including gross domestic product (GDP), industry structure, environmental protection mechanism, urbanization rate, population density, energy consumption intensity and energy consumption structure. Then, we analyzed the internal relevance between the selected three factors and the regional natural gas consumption. Furthermore, we established the GM(1,N) model with fractional order accumulation (FGM(1,N)) to predict the future demand of natural gas consumption in the eastern, central and western areas of China based on the selected three factors. The following results were achieved. (1) Energy consumption structure, GDP, and urbanization rate are three main influencing factors of natural gas demand in the eastern and central areas, while in the western area, the three main factors are urbanization rate, industry structure and population density. (2) In terms of planning natural gas consumption policies, adjustment of energy consumption structure should be strengthened in the eastern area, relationship between economic development and energy consumption should be focused on in the central area, urbanization should be speeded up in the western area. (3) The FGM(1,N) model based on three main factors, well fitting historic demand data, will have a good prediction performance. (4) Natural gas demand in the eastern, central and western areas will achieve a sustainable growth in 2020–2025. However, such growth rate may decrease due to energy reform and external economic environment. By 2025, natural gas demand in these three areas will be about 244 billion cubic meters (bcm), 64 bcm and 100 bcm respectively, with a total value of 408 bcm for the whole China.