A fuel reforming system includes a fuel injection device capable of injecting fuel into an EGR passage, a reforming catalyst provided in the EGR passage, an oxidation catalyst provided in the vicinity of the reforming catalyst in the EGR, and an air supply device that supplies air to the EGR passage. When clogging occurs in the reforming catalyst and a temperature of the reforming catalyst is less than a first temperature, air is supplied to the EGR passage by the air supply device, and fuel is injected by the fuel injection device. When clogging occurs in the reforming catalyst and the temperature of the reforming catalyst is greater than or equal to the first temperature, air is supplied to the EGR passage by the air supply device, and fuel injection of the fuel injection device is stopped.