A steel pipe is formed by performing pipe making of a raw material having a composition containing C: 0.05% or less, Si: 0.50% or less, Mn: 0.20% to 1.80%, P: 0.030% or less, S: 0.005% or less, Cr: 14.0% to 18.0%, Ni: 5.0% to 8.0%, Mo: 1.5% to 3.5%, Cu: 0.5% to 3.5%, Al: 0.10% or less, Nb: more than 0.20% and 0.50% or less, V: 0.20% or less, N: 0.15% or less, and O: 0.010% or less, on a percent by mass basis, wherein Cr+0.65Ni+0.6Mo+0.55Cu−20C≥18.5 and Cr+Mo+0.3Si−43.3C−0.4Mn−Ni−0.3Cu−9N≤11 are satisfied and subjecting the resulting steel pipe to a quenching treatment to heat to a temperature higher than or equal to the Ac3 transformation temperature and, subsequently, cool to a temperature of 100° C. or lower at a cooling rate higher than or equal to the air cooling rate and a tempering treatment to temper at a temperature lower than or equal to the Ac1 transformation temperature.