A complex flow-path heat exchanger having U-shaped tube and cantilever combined coil, which can achieve, in this type heat exchanger, a simple construction, a complex flow of steam within the same one heat exchange shell body, a high heat exchange efficiency, and a low energy loss. The technical gift of the present invention is that, after entering into the heat exchanger, steam firstly effects heat exchange on the U-shaped tube flow path shell side to be cooled and condensed, thereafter entering into flow path tube side of the cantilever combined coil, which are disposed within the same one shell, for a secondary heat exchange, and subsequently flowing out of the heat exchanger after being subcooled. Such steam-water heat exchanger having a complex flow path are advantageous in a small steam flow resistance of the U-shaped tube flow path shell side; a higher condensate water flow velocity in the cantilever combined coils flow path tube; a high heat exchange coefficient; good coordination of the temperature difference fields of the hot and cold fluids in the heat exchanger; and a high heat exchange efficiency. Therefore, the present heat exchanger can be a new generation product relative to the currently-used conventional low-temperature, low-pressure and corrosion-free heat exchangers.