The present invention relates to a method of a washing machine having a tub (21) for holding washing water, a drum (31) rotatably mounted in the tub (21), and a stem generator (51) for generating and supplying steam to the tub (21), for washing laundry with steam, and a washing machine thereof. The method includes a washing water supply step (S 10) for supplying washing water to the tub (21), a steam supply step (S80) for supplying the steam to the tub (21), and a main washing step (S110) for washing the laundry.