A combustion control apparatus of a compression self-ignition internal combustion engine including an exhaust gas recirculation apparatus by which part of exhaust gas discharged to an exhaust system is recirculated into an intake system, and a fuel injection valve configured such that multi-stage divided main injections can be executed as main injection that is fuel injection for obtaining required torque that is determined according to the internal combustion engine operating state, wherein at a time of low-load operation of the internal combustion engine, fuel injections respectively corresponding to: initial slow-burning combustion in which fuel is injected while an encounter rate reduction operation is performed in order to reduce the encounter rate between oxygen and fuel spray in a cylinder so that the fuel is combusted in a state in which an in-cylinder temperature is relatively low; premixed combustion; and diffusion combustion are executed in order as mutually independent multi-stage divided main injections, characterized in that at a time of high-load operation of the internal combustion engine, in a state in which part of exhaust gas is recirculated into the intake system by the exhaust gas recirculation apparatus and in a state in which a pre-heating operation has not been performed before start of the initial slow-burning combustion, continuous main injection is executed, the continuous main injection continuously injecting fuel for a period from before compression top dead center of a piston to after compression top dead center without stopping fuel injection for performing the initial slow-burning combustion and the premixed combustion, premixed combustion is obtained by means of the continuous main injection continued at a low fuel injection rate over a relatively long period wherein the fuel injected in the combustion chamber is cooled by an endothermic reaction with the fuel that is subsequently injected in the combustion chamber while an encounter rate reduction operation is performed in order to reduce the encounter rate between oxygen and fuel spray in a cylinder so that the fuel is combusted in a state in which an in-cylinder temperature is relatively low, diffusion combustion main injection for performing diffusion combustion is executed after the continuous main injection has ended, and a penetration force of fuel injected in the diffusion combustion main injection is set lower than the penetration force of fuel injected in the continuous main injection by setting a fuel injection amount in the continuous main injection higher than a fuel injection amount in the diffusion combustion main injection. wherein at a time of low-load operation of the internal combustion engine, fuel injections respectively corresponding to: initial slow-burning combustion in which fuel is injected while an encounter rate reduction operation is performed in order to reduce the encounter rate between oxygen and fuel spray in a cylinder so that the fuel is combusted in a state in which an in-cylinder temperature is relatively low; premixed combustion; and diffusion combustion are executed in order as mutually independent multi-stage divided main injections, characterized in that at a time of high-load operation of the internal combustion engine, in a state in which part of exhaust gas is recirculated into the intake system by the exhaust gas recirculation apparatus and in a state in which a pre-heating operation has not been performed before start of the initial slow-burning combustion, continuous main injection is executed, the continuous main injection continuously injecting fuel for a period from before compression top dead center of a piston to after compression top dead center without stopping fuel injection for performing the initial slow-burning combustion and the premixed combustion, premixed combustion is obtained by means of the continuous main injection continued at a low fuel injection rate over a relatively long period wherein the fuel injected in the combustion chamber is cooled by an endothermic reaction with the fuel that is subsequently injected in the combustion chamber while an encounter rate reduction operation is performed in order to reduce the encounter rate between oxygen and fuel spray in a cylinder so that the fuel is combusted in a state in which an in-cylinder temperature is relatively low, diffusion combustion main injection for performing diffusion combustion is executed after the continuous main injection has ended, and a penetration force of fuel injected in the diffusion combustion main injection is set lower than the penetration force of fuel injected in the continuous main injection by setting a fuel injection amount in the continuous main injection higher than a fuel injection amount in the diffusion combustion main injection.