A round billet containing, by mass %, 10.50 to 14.00% of Cr with a value represented by the equation of “Cr+4Si−(22C+0.5Mn+1.5Ni+30N)” of not more than 9.0%, wherein the symbols of the elements represent the contents, by mass %, of the elements in the steel, is heated at a soaking temperature of 1100 to 1250 ° C. so that an in-furnace time (min) is not less than “0.5×Diameter of the round billet (mm)”, and then pierced and rolled with a piercing efficiency by a piercing mill of not less than 50%, a value regulated by the equation: “{(Diameter of the round billet−Roll gap at the foremost end of the plug)/Diameter of the round billet} ×100” of not more than 8.0, and a plug shape represented by the equation: “Radius of foremost end of the plug (mm)/Diameter of the round billet (mm)” of 0.06 to 0.17. The thus-manufactured high-Cr seamless steel pipe or tube has excellent internal surface properties with minimized internal surface defects.