A heat exchanger employed as an evaporator includes a heat exchange core section and first to fourth headers 5, 6, 9, 11. The headers 5, 6 include hollow header bodies 10, 20 having opposite ends opened, and caps 18a, 18b, 19a, 19b fixed to the corresponding opposite end openings. The caps 18a, 18b have flat wall portions 32a, 33a, 34a which close the corresponding end openings of the header bodies 10, 20. A reinforcement projection portion 30 projecting toward the interior of the header 5 is formed on the flat wall portion 32a of the cap 18a. In the heat exchanger, the header 5 exhibits enhanced withstand pressure.