An internal combustion engine in which a required reformed-fuel heat generation quantity (required output cylinder heat generation quantity) is calculated based on a required engine power and the thermal efficiency of an output cylinder. An estimated reformed fuel heat generation quantity is calculated based on the molar number of reformed fuel, mole fraction of each gas component in the reformed fuel, and heat generation quantity of each gas component in the reformed fuel. When a value resulting from subtracting the estimated reformed fuel heat generation quantity from the required reformed-fuel heat generation quantity is negative, a fuel reforming operation is not executed, assuming that there is a possibility that surplus reformed fuel may be generated. For example, a fuel supply from an injector to a fuel reformation chamber is stopped.