To obtain a steel small in deterioration of toughness after bending caused by linear heating by preparing a steel having a non-Mo addition type contg. C, Si, Mn or the like in specified ratios.

A non-Mo addition type steel having a compsn. contg., by weight, 0.03 to 0.10% C, ≤0.50% Si and 0.4 to 2.0% Mn, furthermore contg., at need, one or ≥ two kinds of strengthening elements selected from among 0.05 to 0.80% Cu, 0.10 to 3.00% Ni, 0.05 to 1.00% Cr, ≤0.10% V, 0.002 to 0.05% Nb, 0.0005 to 0.0025% B and 0.01 to 0.15% Zr, and the balance substantial Fe is prepd. Furthermore, this steel is produced by heating an ingot or a slab obtd. by casting the steel having the above compsn. to ≥1050°C after the casting, then starting rolling, completing the rolling at a finishing temp. of <850°C, immediately executing water cooling and thereafter subjecting it to air cooling.