A method for continuously producing pipes, each having a polygon-shaped closed cross-section taken perpendicularly to the feeding direction of a strip of metal, which are free from brittleness caused by metal fatigue, and have good precision. A feed-bending method of successively feeding a strip of metal (work) W between a main die body, mandrel,punch and correction punches by predetermined feed lengths,and pressing the work W with these members synchroously with feeding is performed. The work W is gradually bent along designed ridgelines L1 through L2 extending in the feeding direction and defining ridgelines L5 through L8 of a product pipe W1, from the ridgelines L1 and L2 close to widthwise ends e1 and e2 to the ridgelines L3 and L4 in the widthwise center thereof in the course between the vicinity of an inlet and the vicinity of a middle of a device, and then, a resulting rough pipe W0 is corrected from the inside and outside thereof in the vicinity of an outlet of the device.