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The normal supply of energy is related to the stable development of the economy and society. Forecasting energy consumption helps prepare for the normal supply of energy. In the study of energy consumption forecasting, different scholars have used different forecasting models. This paper uses five-year energy consumption data in the Beijing-Tianjin-Hebei region and uses the grey fractional FGM(1, 1) model to analyze the next six years. Then, the energy consumption of three places is predicted. The advantage of the grey score FGM(1, 1) model is that it can get more accurate prediction results based on a small amount of information. In this study, relatively outdated information affects the accuracy of prediction results. However, other prediction models have great limitations on data. Choosing the grey number fractional model for prediction research can get a more reasonable prediction result. We use the FGM(1, 1) model to make predictions and get the prediction results. In Beijing, the growth rate of natural gas consumption has slowed down and will be basically stable by 2023. The average annual deceleration of coal consumption is 32%. The average annual deceleration of coke consumption is 10%. Crude oil consumption decreased by 6.3% annually. Gasoline consumption is slowly increasing. The consumption of kerosene increased about 8% annually. Diesel consumption is slowly decreasing. Fuel oil consumption is reduced by 17% annually. The average annual growth rate of power consumption exceeds 6%. In Tianjin, the annual growth rate of natural gas consumption is about 5%. Coal consumption is reduced by about 8% every year. The average annual deceleration of coke consumption is 7%. Crude oil consumption decreased by 2.4% annually. Gasoline consumption is slowly decreasing. The consumption of kerosene has increased by about 20% annually. Diesel consumption is slowly decreasing. Fuel oil consumption is reduced by 20% annually. Electricity consumption is slowly increasing. In Hebei Province, the annual growth rate of natural gas consumption is about 15%. Annual coal consumption is reduced by about 3%. Coke consumption remained stable. Crude oil consumption is reduced by 3% annually. Gasoline consumption is slowly increasing, and kerosene consumption has increased by about 31% annually. Diesel consumption is reduced by about 3% annually. Fuel oil consumption remained stable. Electricity consumption is slowly increasing. [ABSTRACT FROM AUTHOR]