To prevent a reduction in function of an exhaust gas cooling device caused by troubles at an end part of an exhaust gas passage such as a heat transfer pipe and the like.

Since a heat transfer pipe 6 has its end part expanded in a tapered form, a flow of exhaust gas from an opening 6b to an exhaust space region 14 is once expanded just after being discharged out of the opening 6b, its flow speed is not decreased rapidly, but it is gradually expanded in a continuous manner within an exhaust gas passage 17 while it reaches up to the opening 6b. Accordingly, since no rapid reduction in flow speed occurs in the exhaust gas flow, it is possible to attain a sufficient restriction of accumulation of carbon within the opening 6b of the exhaust gas passage 17. In this way, a sufficient flow passage area can be assured at the exhaust gas passage 17, a requisite amount of exhaust gas can be sufficiently cooled and supplied to an intake system of an internal combustion engine through an EGR valve. Accordingly, it is possible to prevent the function of the exhaust gas-cooling device caused by the accumulation of carbon.