A driving force transmission apparatus is provided for a twin clutch transmission with two clutches, that are controlled a gear change control without a torque cutting out to reduce slapping sounds of the gears by performing a pre-shift operation before the gear shift control. For instance, in an up-shift operation from second speed to third speed, the clutch that transmits torque to the third speed gear set is slip-engaged and one gear of the third speed gear set is connected through a synchronous engagement device to a countershaft. During the pre-shift, a sub torque transmission path that is formed transmits engine torque of the engine, a crankshaft, the clutch, a first input shaft, the third speed gear set, the countershaft, and a differential gear system, preventing the first input shaft from becoming idle and the slapping sound of the gears in an engagement part of the third speed gear set.