A driving system for a washing machine having a washing shaft connected with an agitator in the center of a washing tub to stir laundry in washing mode, and an extracting shaft positioned outside the washing shaft and connected with an extracting tub which rotates at high speeds in extracting mode, further includes a power generator for generating power to rotate the washing shaft and the extracting shaft, a decelerator installed under the power generator to reduce the number of rotation transmitted from the power generator, and a power-switching device for de-energizing the extracting shaft in washing mode and for energizing the extracting shaft in extracting mode.