A control device for an internal combustion engine for controlling an internal combustion engine provided with: an engine body; and a fuel injector injecting fuel into a combustion chamber of the engine body, the control device comprising a combustion control part configured to: sequentially inject at least a primary auxiliary fuel, secondary auxiliary fuel, and main fuel from the fuel injector in predetermined operating regions, after start of injection of the main fuel, cause sequentially compressive ignition from a premix containing the primary auxiliary fuel, compressive ignition from a premix containing the secondary auxiliary fuel and compressive ignition of a premix containing the main fuel using heat generated when causing compressive ignition of the premix containing the secondary auxiliary fuel, to set a target injection amount and target injection timing of the primary auxiliary fuel so that a peak value and a slant at the start of combustion of a heat generation rate pattern formed by the premix containing the primary auxiliary fuel is smaller than respective peak values and slants at the start of combustion of heat generation rate patterns formed by the respective premixes containing the secondary auxiliary fuel and the main fuel, and to set the target injection amount and target injection timing of the primary auxiliary fuel so that the premix containing the primary auxiliary fuel first burns by compressive ignition after an equivalent ratio of the premix becomes less than 1. an engine body; and a fuel injector injecting fuel into a combustion chamber of the engine body, the control device comprising a combustion control part configured to: sequentially inject at least a primary auxiliary fuel, secondary auxiliary fuel, and main fuel from the fuel injector in predetermined operating regions, after start of injection of the main fuel, cause sequentially compressive ignition from a premix containing the primary auxiliary fuel, compressive ignition from a premix containing the secondary auxiliary fuel and compressive ignition of a premix containing the main fuel using heat generated when causing compressive ignition of the premix containing the secondary auxiliary fuel, to set a target injection amount and target injection timing of the primary auxiliary fuel so that a peak value and a slant at the start of combustion of a heat generation rate pattern formed by the premix containing the primary auxiliary fuel is smaller than respective peak values and slants at the start of combustion of heat generation rate patterns formed by the respective premixes containing the secondary auxiliary fuel and the main fuel, and to set the target injection amount and target injection timing of the primary auxiliary fuel so that the premix containing the primary auxiliary fuel first burns by compressive ignition after an equivalent ratio of the premix becomes less than 1. sequentially inject at least a primary auxiliary fuel, secondary auxiliary fuel, and main fuel from the fuel injector in predetermined operating regions, after start of injection of the main fuel, cause sequentially compressive ignition from a premix containing the primary auxiliary fuel, compressive ignition from a premix containing the secondary auxiliary fuel and compressive ignition of a premix containing the main fuel using heat generated when causing compressive ignition of the premix containing the secondary auxiliary fuel, to set a target injection amount and target injection timing of the primary auxiliary fuel so that a peak value and a slant at the start of combustion of a heat generation rate pattern formed by the premix containing the primary auxiliary fuel is smaller than respective peak values and slants at the start of combustion of heat generation rate patterns formed by the respective premixes containing the secondary auxiliary fuel and the main fuel, and to set the target injection amount and target injection timing of the primary auxiliary fuel so that the premix containing the primary auxiliary fuel first burns by compressive ignition after an equivalent ratio of the premix becomes less than 1.