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Energy consumption in the world is mainly dependent on fossil energy, and oil is one of the main energy sources. Accurate prediction of oil consumption can provide an important basis for national energy security, which can provide reference and early warning for the implementation of the environmental strategy developed by the government. According to the nonlinearity of the energy system, this paper uses the principle of the grey nonlinear prediction model NGBM(1,1) to improve the background value of the model, and by the simulated annealing algorithm, we put forward the optimized grey nonlinear model ONGBM(1,1). At the same time, the model is applied to the oil consumption of China, Chile, Mexico, and Japan. Based on the validity analysis of the existing data of the four countries, the model ONGBM(1,1) is basically superior to the other six grey forecast models. Finally, ONGBM(1,1) is used to predict the oil consumption of the four countries in the next five years, which can provide effective information for energy economic policy. [ABSTRACT FROM AUTHOR]