To prevent a plate 14, etc. within a unit U from corroding by condensate.

An EGR cooler 1 includes an inner tube 2, an outer tube 4, and a coolant passage 3, and the heat of exhaust gas G circulating in the inner tube 2 is conducted to coolant W circulating in the coolant passage 3. The inner tube 2 is composed of four units U, and each unit U houses a plate 14 in its large-diameter part 12. The plate 14 and connections 13A and 13B in its upper and lower positions are made in the shape of cones the centers of which are lower than their peripheries, and a drain hole 14A is bored at the center of the plate 14. When condensate by exhaust gas G arises in the unit U, the condensate is discharged downward from the drain hole 14A after adhering onto the plate 14.