The invention relates to an electric motor driven vehicle having a driving unit assembled with a motor and transmission mechanism. In order to avoid a load in a low rotational state of the motor, the transmission mechanism is connected with the motor and driving wheel within a range of predetermined rotational numbers in which the motor approaches the vicinity of maximum efficiency. Accordingly, motor driving is possible from the start, and because of the small electric power and the low heat generating quantity, cruising distance is extended and the apparatus is consequently made to be compact and of light weight. The transmission is provided with an automatic starting clutch and an automatic transmission is used as the automatic transmission, operation of the motor near the vicinity of maximum efficiency can always be maintained in the usual speed change range. The driving unit can be constructed compactly as a power unit of swing type. Further, an advantageous cooling mechanism of the motor and a wiring structure of an electric power supply cord are disclosed herein.