To provide a control method which provides excellent operation efficiency in an internal combustion engine for Miller cycle operation.

Miller cycle operation is performed in light load and Otto cycle operation is performed in heavy load. Two kinds of fuel of different octane numbers can be supplied at an optional mixing ratio, and intake air temperature is adjusted. As the intake air temperature gets higher, the octane number is set higher. As the intake air temperature gets lower, the octane number is set lower. As the load gets heavier, the octane number is set higher. As the load get lighters, the octane number is set lower. The two kinds of fuel are gasoline and ethanol, or gasoline and ethanol-water mixture separated from mixed fuel of gasoline and ethanol by adding and mixing water to the mixed fuel. When a remaining quantity of fuel of low octane number is low, the temperature of intake air is raised and the octane number of fuel is raised. When a remaining quantity of fuel of high octane number is low, the temperature of intake air is dropped and the octane number of fuel is dropped.

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