To take advantage of a merit of a premixed compression ignition internal combustion engine by reducing discharge amounts of a harmful exhaust gas (NOx) and soot.

This combustion method and this combustion structure are used for injecting a plurality of kinds of combustible air-fuel mixtures into a combustion chamber. The injection is carried out by stratifying the temperature of the air-fuel mixtures while homogenizing concentration of the combustible air-fuel mixtures with a plurality of fuels mixed with air. Thereby, the combustible air-fuel mixtures injected into the combustion chamber have the same concentration and a plurality of kinds of combustible air-fuel mixtures having different octane numbers are used. A structure making mixture of the plurality of kinds of injected combustible air-fuel mixtures difficult is formed in the combustion chamber being one space.