Seamless pipes excellent in quality features with high productivity is made by a by carrying out piercing-rolling using a piercer provided with a pair of inclined rolls. The piercing-rolling is carried out under conditions such that the plug tip draft (TDFT) or the root of the product of the plug tip draft (TDFT) are controlled along with the number of billet revolutions (N), namely (TDFT×N)0.5. In addition, positions of the inclined rolls are controlled in connection with the gorge draft (GDFT) indicating the ratio of the roll gap (Rg) which is minimal in the gorge section between the inclined rolls to the billet outside diameter (Bd). The piercing-rolling is carried out using a plug having a particular shape.