A drum driving device for a window shade comprising a housing fixed to a frame of the window shade, a cord pulley rotatably received in the housing and having a cord wound around the cord pulley, a drum rotatably mounted to a drum shaft received in the housing, and a single-direction clutch device mounted between the drum and the cord pulley, wherein: the clutch device includes a chamber defined in the housing and coaxial to an axis of the housing, a driving shaft coaxially mounted to the cord pulley, a transmission shaft mounted in the chamber, and a driving spring 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 driving 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, with the cord pulley including a coaxial positioning axle to which the transmission shaft is mounted, with the positioning axle including a positioning ring on an end face of the positioning axle, with a spacing between the end face of the positioning axle and an end face of the driving shaft being slightly larger than a spacing between the end face of the driving shaft and an end face of an axial hole of the transmission shaft facing the end face of the driving shaft, with the outer diameter of the transmission shaft is slightly smaller than that of the driving shaft, characterized by the transmission shaft including an inner transmission shaft rotatably mounted to the positioning axle, the transmission shaft further including an outer transmission shaft coupled to the inner transmission shaft, the inner transmission shaft including the axial hole and a transmission ring, the transmission ring including an insert end, the outer transmission shaft including a connecting head having a groove, the insert end engaged in the groove, the outer transmission shaft further including a rotary head extending out of the chamber, the rotary head coupled to a drum driving shaft, and the drum driving shaft having a connecting block coupled to the drum shaft. the clutch device includes a chamber defined in the housing and coaxial to an axis of the housing, a driving shaft coaxially mounted to the cord pulley, a transmission shaft mounted in the chamber, and a driving spring 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 driving 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, with the cord pulley including a coaxial positioning axle to which the transmission shaft is mounted, with the positioning axle including a positioning ring on an end face of the positioning axle, with a spacing between the end face of the positioning axle and an end face of the driving shaft being slightly larger than a spacing between the end face of the driving shaft and an end face of an axial hole of the transmission shaft facing the end face of the driving shaft, with the outer diameter of the transmission shaft is slightly smaller than that of the driving shaft, characterized by the transmission shaft including an inner transmission shaft rotatably mounted to the positioning axle, the transmission shaft further including an outer transmission shaft coupled to the inner transmission shaft, the inner transmission shaft including the axial hole and a transmission ring, the transmission ring including an insert end, the outer transmission shaft including a connecting head having a groove, the insert end engaged in the groove, the outer transmission shaft further including a rotary head extending out of the chamber, the rotary head coupled to a drum driving shaft, and the drum driving shaft having a connecting block coupled to the drum shaft.