PURPOSE: To produce a seamless stainless steel tube excellent in corrosion resistance by subjecting a stainless steel containing the specific amounts of C, Si, Mn, P, S, Cr, Mo, Ni, Al, and N to a heat treatment in specific conditions.

CONSTITUTION: A steel which has a composition consisting of, by weight, ≤0.05% C, ≤0.5% Si, ≤1% Mn, ≤0.03% P, ≤0.01% S, 11-15% Cr, 0.3-2% Mo, 1.5-5% Ni, ≤0.05% Al, 0.02-0.1% N, and the balance essentially Fe and satisfying C%+0.8N%>0.06 is hot-worked, subjected to natural air cooling down to a room temp., heated up to a temp. in the range between (AC3 transformation point +10°C) and (Ac3 transformation point +200°C), cooled down to the room temp. at the rate not lower than air cooling rate, and successively subjected to a tempering treatment at a temp. not higher than the Ac1 transformation point. By this method, the seamless tube of martensitic stainless steel excellent in CO2 corrosion resistance, sulfide stress corrosion cracking resistance, and hot workability is produced.