The invention discloses a gear speed reduction device. The gear speed reduction device comprises a rotating-shaft-free rotator for providing rotating kinetic energy, a speed reduction input component installed in the rotator, a speed reduction output component connected with the speed reduction input component, a first execution component and a second execution component, wherein the first execution component and the second execution component are connected with the speed reduction output component. The speed reduction input component is used for obtaining the rotating kinetic energy and rotating relative to the axis of the rotator by utilizing the obtained rotating kinetic energy; the speed reduction output component is used for outputting power with the rotating speed equal to or lower than the rotating speed of the rotator; and the first execution component and the second execution component are used for rotating under the power effect of the speed reduction output component. A speed reducer is installed in the rotator, and accordingly the volume of the whole gear speed reduction device is compressed. Besides, the gear speed reduction device is simple and compact in structure, saves energy and is small in noise. The invention further provides a washing machine with the gear speed reduction device and a washing method thereof.