A steel pipe for an airbag inflator having a high strength of at least 900 MPa and preferably at least 1000 MPa in tensile strength along with a high toughness and exhibiting good resistance to bursting such that it has no propagation of cracks in a burst test at -40.degree. C. or below is manufactured by quenching a pipe of a steel comprising, in mass %, C: 0.05-0.20 %, Si: 0.1-1.0 %, P: at most 0.025 %, S: at most 0.010 %, Cr: 0.05-1.45 %, Al: at most 0.10 %, and one or both of Ti and Mn satisfying Ti.ltoreq.0.02% and 0.4%.ltoreq.Mn+40Ti.ltoreq.1.2% from a temperature of at least the Ac.sub.1 transformation point of the steel, tempering the pipe at a temperature lower than the Ac.sub.1 transformation point, applying cold working to it with a reduction of area of at most 65%, and subjecting it to stress relief annealing at a temperature lower than the Ac.sub.1 transformation point. The ratio L/T of the X-ray integrated intensity ratio of the {110} plane measured for the cross section perpendicular to the axial direction L of the steel pipe to that measured for the cross section perpendicular to the circumferential direction T is at most 50.