A double-tube heat exchanger that is easy to produce, the entire part of which is smoothly bent so that the heat exchanger works as a part of piping, and that has high pressure resistance. In the cross-section perpendicular to the axis of an inner tube (1), there are bag-like or ballon-like bulged sections (7a) directing radially from the center, and openings of the bulged sections (7a) are closed and the head of each bulged section (7a) is in contact with the inner surface of an outer tube (2).