A drum driving device for a window shade includes a housing fixed to a frame of the window shade. A cord pulley is rotatably received in the housing. A drum is rotatably mounted to a drum shaft received in the housing A single-direction clutch device is mounted between the drum and the cord pulley. The clutch device includes a chamber defined in the housing. A driving shaft is coaxially mounted to the cord pulley. A transmission shaft is mounted in the chamber. A driving spring is mounted to an inner periphery of the chamber and around the driving shaft and the transmission shaft in the chamber. The transmission shaft has an outer diameter not larger than that of the transmission shaft. The driving spring is in tight contact with the driving shaft and the inner periphery of the chamber. The transmission shaft is extended out of the chamber and connected to the drum.