PURPOSE: To reduce the number of the production steps of the heat exchanger by a method wherein one sheet is cut in a predetermined shape and bent to define wide trapezoid zones and narrow trapezoid zones and also define ventilating passages alternately in the circumferential direction.

CONSTITUTION: The elongated sheet 2 is defined into wide trapezoid heat exchanging zones 3a, 3b... and closed end surface parts 4a, 4b... by lines 5a, 5b, 6a, 6b.... The heat exchanging zones 3a, 3b... have on the short side flaps 8a, 8b... separated by a notch 7. Then, the sheet 2 is bent along the lines 5a, 5b and 9b at the base of the flap 8b in a V-shape, and along the lines 6a, 6b and 9a at the base of the flap 8a in an upside-down V-shape, so that the ventilating passages 10 and 11 having end openings 10a and 11a and side openings 10b and 11b are formed in contact with the flaps (8a, 8a) and (8b, 8b). Within the central hollow space of thus formed heat exchanger body in a ring, there is inserted a cylinder. Further, another cylinder is put over the outer periphery of the heat exchanger body and then the area of the openings 10b, 11b is properly adjusted.