An internal combustion engine in which when the gas temperature of a fuel reformation chamber when a piston in a fuel reformation cylinder reaches the compression top dead point is estimated to be equal to or higher than a soot generation lower limit temperature set according to an equivalence ratio of the fuel reformation chamber, a reaction gas temperature adjusting operation for suppressing or reducing an increase in the reaction gas temperature in the fuel reformation chamber is executed. Further, a closing timing of an air-intake valve is changed to reduce an effective compression ratio of the fuel reformation chamber.