NOVELTY - The power supply device has a battery case engagement part that is offset to one side of the battery case from the lateral center of the vehicle in a state where the battery case is mounted on the electric vehicle. The battery case engagement part is formed at each of the front and rear side portions of the battery case relative to the vehicle, in order that the battery case engagement part can fit to the vehicle body engagement part (59). The vehicle body engagement is offset to one side from lateral center of vehicle.    USE - Power supply device for an electric vehicle e.g. electric motorcycle.    ADVANTAGE - The battery pack is free of protruding parts and the battery pack can be tentatively positioned with a simple structure. The battery case side engagement recess includes a wall part coinciding generally with a locus of movement of the peak portion of the engagement projection, in the course of inclining the battery case from the tentatively placed position to a completely mounted position such that it ensures that when the battery case is tilted from the tentatively placed position to the completely mounted position, the change in posture can be achieved by putting the peak portion of the engagement projection along the wall part of the battery case engagement part. Visual checking of the positional relationship between the battery case engagement parts and the vehicle body engagement part is not obstructed by the battery pack cover when mounting the power supply device to the vehicle. The lower open end portion of the engagement recess makes contact with the upper surface of the shelf protruding horizontally from the terminal base such that the power supply device can easily be mounted and detached.    DESCRIPTION OF DRAWING(S) - The drawing shows a perspective view of a terminal base fixed to the battery pack cover, as viewed from a right upper rear side of the vehicle body.    Battery pack cover (28)    Terminal base (29)    Vehicle body engagement part (59)    Harness (65)    Central engagement projection (66)