A steel pipe for an air bag inflator which has a high strength of a tensile strength of 900 MPa or more, preferably 1000 MPa or more, together with high toughness, and exhibits good burst resistance wherein no cracks develop in a burst test at -40 DEG C or lower is produced by a method comprising providing a raw steel pipe containing, in mass %, 0.05 to 0.20 % of C, 0.1 to 1.0 % of Si, 0.025 % or lower of P, 0.010 % or lower of S, 0.05 to 1.45 % of Cr, 0.10 % or less of Al, 0.02 % or less of Ti, and one or both of Ti and Mn satisfying 0.4 = Mn + 40 X Ti = 1.2, rapidly cooling the raw steel pipe from a temperature of Ac1 transformation temperature or higher, tempering the resultant steel pipe at a temperature lower than Ac1 transformation temperature, subjecting the tempered steel pipe to a cold working wherein a reduction of area is 65 % or less, and then subjecting the worked steel pipe to a stress relief annealing at a temperature lower than Ac1 transformation temperature. The L/T ratio of X ray integral intensity ratios of {110} face measured in the cross section perpendicular to the axis direction (L) and the cross section perpendicular to the periphery direction (T) of the above steel pipe is 50 or lass.