PURPOSE: To produce a carbon steel having strength at high temp. without deteriorating weldability by subjecting the steel with specific composition up to a temp. not lower than austenitizing temp. and then to continuous hot working at a temp. in a specific temp. region.

CONSTITUTION: The steel has a composition consisting of, by weight, 0.03-0.15% C, ≤1.0% Si, 0.5-1.5% Mn, ≤0.03% P, ≤0.03% S, 0.1-0.5% Cr, 0.05-0.3% Mo, ≤0.01% Al, 0.005-0.03% N, and the balance Fe with inevitable impurities. The steel is heated up to a temp. not lower than the austenitizing temp. and continuously hot-worked in the temp. region between a temp. higher than Ar3 and a temp. right above Ar1 in the course of cooling. By this method, strength at high temp. can be obtained in the ranges of the components causing no deterioration in weldability.