An EGR cooler has tubes and a shell for enclosing the tubes. Cooling water is supplied into and discharged from the shell and exhaust gas from a diesel engine is guided into each of the tubes so as to conduct heat exchange of the exhaust gas with the cooling water. An inner periphery of each of the tubes is formed with spiral protrusions each having an inclination angle in a range of 26.degree. 50.degree. to a plane perpendicular to an axis of the tube.