The present invention relates to a heating device for exhaust gas in an internal-combustion engine, which is driven by using LPG, LNG, a volatile oil, a light oil, biodiesel or oxygenated hydrocarbon being DME, the device consisting of a catalyst reactor reformer, an exhaust gas suction section and the second fuel supply device. The exhaust gas suction section is mounted for using oxygen included in the exhaust gas. When the heating device is driven, air and fuels are supplied to the catalyst reactor and the second fuel supply device via a single tube when the heating device is heated. The present invention provides with a heating device for exhaust gas capable of securing the durability of a heating device for exhaust gas and minimizing the amount of air supplied from the outside to the combustion reforming device by excluding carbon depositions in a tube due to a prolysis of LPG, LNG, a volatile oil, a light oil, biodiesel or oxygenated hydrocarbon being DME, and a method for driving the device.