In quenching , where a heated steel pipe (2) is immersed in a water bath (3) in parallel with water surface for cooling a pipe outer surface, and cooling water is injected from an axial center nozzle (8) into one end of pipe for cooling a pipe inner surface, thereby rapidly cooling the entire pipe surface,, reduction of strength difference along a length of the quenched pipe becomes possible by moving the nozzle (8) following the motion of the pipe axis (2), and starting injecting the water from the nozzle (8) so as for the water to reach the other pipe end at the time of the immersion of the entire circumference of the pipe outer surface. An opening (3a) preferably faces the nozzle (8) to remove the water, and the flow velocity is preferably set to 23 m/sec or more for better water flow inside the pipe (2).