To produce a low alloy seamless steel tube excellent in toughness and high temp. creep rupture strength by executing heat treatment on a tube producing line.

A billet contg. 0.04 to 0.20% C, ≤1.0% Si, 0.1 to 1.5% Mn, 0 to 3.5% Cr, 0 to 2.5% Mo, and the balance Fe with inevitable impurities is heated and is subjected to hot perforation and rolling to produce a seamless steel tube. At this time, succeeding to the perforating, the operation of executing finish rolling of ≥40% cross-section compressibility at 800 to 1,100°C, thereafter immediately executing reheating normalizing treatment at the temp. T in the temp. range of 850 to 1,100°C for the time (t) so as to regulate the value of (f)1 shown in the equation, (f)1=(T+273)×(21+logt) [wherein, T is (°C) and (t) is (hr)] to 23,500 to 26,000 and next executing tempering treatment at the Ac1 point or below is continuously executed on line.