In an oil cooler, a heat exchange core is housed in a casing including a cylindrical sidewall part in a way that a cooling water passage is formed around a heat exchange core. The heat exchange core includes inlet-side and outlet-side oil passages, and enables oil to be delivered from the inlet-side oil passage to the outlet-side oil passage. Inlet and outlet pipes are connected to the sidewall part. The inlet pipe forms a cooling water inlet passage in communication with the cooling water passage. The outlet pipe forms a cooling water outlet passage in communication with the cooling water passage. Outward of the inlet-side oil passage, an outwardly swelling part is formed in the sidewall part of the casing. This arrangement avoids the oil cooler being constructed in a large size and avoids decreasing the heat exchange efficiency of the oil cooler, and also prevents cavitation and erosion from occurring due to the flow of cooling water in an area corresponding to the inlet-side oil passage.