A fuel reformer includes a reforming-fuel injection valve and a fuel reformer catalyst disposed in an EGR pipe and performs a catalyst recovery control when a preset fuel cut execution condition is satisfied. In the catalyst recovery control, a fuel reforming capacity of the fuel reformer catalyst is recovered by stopping an injection of a main fuel and an injection of a reforming-fuel, while supplying additional air to the catalyst by maintaining both of an EGR valve and a throttle valve in a valve open state. Further, in the catalyst recovery control, temperature and a carbon deposit amount of the fuel reformer catalyst are estimated or detected based on which of an opening of the EGR valve and an opening of the throttle valve are adjusted. As a result, fuel reforming capacity is recovered without decreasing a fuel consumption rate improvement effect and a worsening of exhaust emission or drivability.