A motor drive apparatus for a vehicle is provided which can prevent its transmission and motor from being rotated by vehicle wheels, and which allows quick gear change. This apparatus includes an electric motor (10), a first shaft (21) driven by the electric motor (10), a second shaft (22), first and second reduction gear trains (23 and 24) disposed between the first and second shafts (21 and 22). Two-way roller clutches (30A and 30B) are mounted between a first output gear (23b) of the first reduction gear train (23) and the second shaft (22) and between a second output gear (24b) of the second reduction gear train (24) and the second shaft (22), respectively. Gear changes are made by selectively engaging and disengaging the two-way roller clutches (30A and 30B) with a speed changing mechanism (50).