A starting material to be extruded made of a high alloy comprising, in mass %, Cr: 20 to 30% and Ni: more than 22% and 60% or less is heated to a temperature predetermined according to the contents of Mo and W and is subjected to a hot-extrusion process, the heating temperature T (° C.) satisfying a relationship of Formula (1), (2), or (3), which is expressed in terms of the average cross-sectional area A (mm2) of the starting material to be extruded, the extrusion ratio EL (−), and the extrusion speed V (mm/s). As a result, a high-alloy seamless tube can be produced without generating cracking and/or seam flaws. When 0%≦Mo+0.5W