There is provided a production method capable of forming spiral ribs stably by reducing troubles at the time of cold drawing for forming the spiral ribs on an internally ribbed steel tube. When the internally ribbed steel tube on which a plurality of stripes of spiral ribs are formed in the tube axis direction is manufactured by inserting a plug on which a plurality of stripes of spiral grooves are formed on the outer peripheral surface thereof into the tube to be worked subjected to chemical treatment and then performing cold drawing, drawing is performed with the plug preheated to 50 to 200° C., thus forming the spiral ribs on the internal surface of a blank tube. The chemical treatment preferably includes a pickling step of removing oxided scale and rust on the tube surface, a step of forming a zinc phosphate coat on the neutralized tube surface, and a step of forming a lubricating layer on the zinc phosphate coat. The internally ribbed steel tube thus obtained is well applicable to increased capacity and higher temperature/higher pressure of a boiler because the steel tube is provided with formability and quality excellent as a boiler steel tube.