A home laundry machine (1) having an outer casing (2) and, inside said casing (2), a laundry container (3, 5) for housing the laundry to be dried, and a steam generator (15) for feeding a given amount of steam into the laundry container (3, 5), and which in turn has a tubular vaporizer (16) containing a given amount of water; a heater (19) for boiling and converting the water in said tubular vaporizer (16) into steam; and a steam exhaust pipe (20) for feeding the steam produced in the tubular vaporizer (16) into the laundry container (3, 5), and which has at least one tubular portion (20a) contacting the heater (19), so that the steam flowing along the tubular portion (20a) receives a certain amount of heat from said heater (19).