A fuel reformer including a first pipe, a second pipe which is disposed in the first pipe, a main heat source, which includes an oxidation catalyst, filling the second pipe adapted to generate thermal energy with a predetermined temperature range through an oxidation reaction of a fuel using the oxidation catalyst; an auxiliary heat source which includes a torch connected to the second pipe to ignite and burn the gaseous fuel, thereby preheating the oxidation catalyst to within a reaction starting temperature range, and a reforming reaction unit which includes a reforming catalyst filling a space between the first and second pipes to generate a reforming gas containing hydrogen through the reforming reaction of the fuel using the reforming catalyst by using the thermal energy generated by the main heat source.