In order to manufacture a steel pipe for an air bag which can cope with increase in the pressure of gas blown into an air bag and decreases in the wall thickness of an accumulator, a steel having a composition, mass %, of: C: 0.05-0.20%,Si: 0.1-1.0%,Mn: 0.20-2.0%, P: at most 0.025%,S: at most 0.010%,Cr: 0.05-1.0%, Al: at most 0.10%, if necessary at least one of Mo: at most 0.50%, Ni: at most 1.5%, Cu: at most 0.5%, V: at most 0.2%, Ti: at most 0.1%, Nb: at most 0.1%, and B: at most 0.005%, andalso if necessary, at least one of Ca: at most 0.01%, Mg: at most 0.01%, and REM (rare earth elements): at most 0.01%,and a remainder of Fe and impurities is used to produce a steel pipe, and the pipe is then subjected to cold working to predetermined dimensions, then to heating to a temperature of at least the Ac1 transformation temperature followed by quenching, and then to tempering at a temperature no higher than the Ac1 transformation temperature.