A method for driving a washing machine that includes a main body, a tub disposed within the main body, a main drum rotatably mounted in the tub, a sub drum mounted in the main drum to be relatively rotatable with respect to the main drum, a driving motor, and a control unit to control operations of the driving motor includes producing a three-dimensional motion of laundry in the washing machine by moving the laundry in a circumferential direction and an axial direction simultaneously by relative motions of the main drum and the sub drum to perform the washing process while supplying washing water and detergent.