To stably reform an unutilized heavy oil without causing choking by coking.

The unutilized heavy oil is fed into a cylindrical body for reaction with a heavy oil feed pipe 17 passing through a vessel wall of a reaction vessel 11, communicating with and connecting to the cylindrical body 23 for the reaction. When the unutilized heavy oil is fed, high-pressure water is fed to a first high-pressure water feed pipe 31 covering the heavy oil feed pipe and extending into the reaction vessel to thereby cool the heavy oil feed pipe and cool the outer surface of the cylindrical body for the reaction with the high-pressure water. The unutilized heavy oil is reacted with supercritical water or subcritical water in the cylindrical body for the reaction having the cooled outer surface and converted into a reformed oil. The resultant reformed oil converted in the cylindrical body 23 for the reaction is discharged from the cylindrical body 23 for the reaction and the reaction vessel 11 with a reformed oil discharge pipe 18 passing through the vessel wall of the reaction vessel, communicating with and connecting to the cylindrical body for the reaction. When the reformed oil is discharged, the reformed oil discharge pipe 18 is cooled by feeding the high-pressure water to a second high-pressure water feed pipe 32 covering the reformed oil discharge pipe 18 and extending into the reaction vessel 11.