A method of manufacturing a high pressure fluid supply pipe of a double pipe structure in which an outer pipe is tightly fit over the outer circumference of an inner pipe, wherein the method comprises a step of forming a double pipe by tightly fitting an inner pipe with an outer pipe having a thermal expansion coefficient greater than that of the inner pipe while putting a brazing material therebetween, and a step of subjecting the double pipe to a heat treatment and then to a gradual cooling treatment to join and tightly fit the inner pipe and the outer pipe integrally to each other, thereby providing at least the inner surface of the inner pipe with a compressive residual stress. The resistance to high inner pressure can be improved and destructive strength, in particular, fatigue resistance to the repeated inner pressure can remarkably be improved.