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An accurate and objective prediction of coal consumption is important for stabilizing the coal market, ensuring the operating results of coal enterprises. This paper starts with the background value of the traditional GM(1,1) model, extends the model by the extrapolation method, proposes an optimized grey prediction model, deduces the time response equation, studies the relationship between model parameters and model accuracy. Then the model is optimized by simulated annealing algorithm. Three cases verify the validity of model, the results show that its lowest prediction error percentage is 3.1286%, which is better than two classical grey prediction models, Finally, the model is applied to forecast the next five years' consumption of China, India and the United States, which are the world's top three coal consumers. The errors of the proposed models are all about 5%, which is obviously better than the comparison models. The results show that coal consumption in China and India will continue to rise over the next five years, while the United States will decline. These findings are consistent with the current development of the three countries; therefore, the optimized prediction model can effectively predict the coal consumption of the three countries. • The highlights of this article are as follows: • An optimized grey prediction model that can be applied to various data situations is proposed. • The traditional GM(1,1) model is optimized by a simulated annealing algorithm. • The validity of the model is verified by theoretical deduction and case analysis. • The generality and wide applicability of the proposed method are discussed. [ABSTRACT FROM AUTHOR]