NOVELTY - The method involves preparing a corrugated metal tube (7) e.g. corrugated iron tube, including a corrugated portion (3) with corrugation hills and valleys, and constructing a flexible outer peripheral portion (9) by forming an elastic rubber layer on an outer periphery of the tube and providing a reinforcing layer (27) on an elastic layer's outer periphery. The tube is plastically deformed outwardly by exerting deforming pressure beyond a yield point of the tube in an inside of the tube, where the pressure is applied such that the hills have Vickers hardness greater than that of the valleys.    USE - Method for making a composite hose that is utilized for conveying fuel such as petrol to engine, carbon dioxide gas refrigerant, and fuel cell hydrogen gas, of a motor vehicle i.e. automobile.    ADVANTAGE - The method enables making shape of the corrugation hills similar to shape of the corrugation valleys by equalizing curvature radius of the corrugation hills and the corrugation valleys when the corrugation hills are deformed in an expanding manner by applying a prepressurizing process to a composite hose with the corrugated metal tube so as to enhance durability of the metal tube effectively against repeated bending deformations and repeated internal pressures, thus preventing damage such as bursting even when the metal tube is used for a long term in an environment in which high pressure is exerted repeatedly by an internal fluid while reducing nonuniformity of durability of the composite hose by maintaining uniformity of restraining functions when the corrugated metal tubes are plastically deformed and even when the reinforcing layer has nonuniform restraining functions.    DESCRIPTION OF DRAWING(S) - The drawing shows a sectional view of a composite hose with a corrugated metal tube that is not plastically deformed.    Composite hose (1)    Corrugated portion (3)    Corrugated metal tube (7)    Flexible outer peripheral portion (9)    Reinforcing layer (27)