A steam generator, used in a helical coil type steam generator for a sodium-cooled fast reactor which has heat transfer tubes of a double-wall tube structure, with high heat transfer efficiency and a heat transfer tube damage detection unit that can detect on-line in real-time whether the heat transfer tube is damaged or not. The heat transfer tube of a steam generator for a sodium-cooled fast reactor, includes an inner tube formed with a first material; an outer tube formed with a second material that is in close contact with the inner tube and which has a thermal expansion coefficient less than that of the first material; and a plurality of helium flow grooves formed between the inner tube and the outer tube along a lengthwise direction of the heat transfer tube for flowing helium gas. The inner tube and the outer tube are identically due to heat for the temperature difference generated during normal operation of the steam generator, so the degree of close contact between the inner tube and the outer tube does not decrease, and the decrease of heat transfer efficiency can be prevented.