PURPOSE: To produce an oil well steel pipe having high strength and excellent in sulfide stress corrosion cracking resistance by subjecting a pipe made of low alloy steel with specific composition to hardening and tempering under respectively specified temp. conditions.

CONSTITUTION: An ingot of a low alloy steel having a composition containing, by weight, 0.20-0.30% C, 0.10-1.50% Si, 0.40-1.50% Mn, <0.015% P, <0.005% S, 0.30-1.20% Ni, 0.50-1.50% Cr, 0.10-2.00% Mo, 0.001-0.10% Al, 0.0005-0.0050% B, <0.005% N, and further one or ≥2 kinds among 0.01-0.10% Ti, 0.01-0.10% Nb, and 0.01-0.10% V is cogged, which is formed into a seamless steel pipe by means of hot rolling by a Mannesman process. This steel pipe is hardened from a temp. not lower than the Ac3 transformation point of this steel and tempered at 600-750°C. By this method, the steel pipe having (63 to 87)kgf/mm2 yield strength, increased in threshold of stress intensity factor in a sulfide environment, and excellent in sulfide stress corrosion cracking resistance required of the steel tube for oil well or gas oil use in a sour environment can be obtained.