A power transmission apparatus for an electric vehicle including a motor as a power source may include: a compound planetary gear set formed as a combination of first and second planetary gear sets sharing a sun gear and a plurality first pinion gears; a first brake selectively connecting a first ring gear of the first planetary gear set to a transmission housing; and a second brake selectively connecting the shared sun gear of the first and second planetary gear sets to the transmission housing. In particular, a second ring gear of the second planetary gear set is fixedly connected to a rotor of the motor and thus continuously receives a torque of the motor, and the power transmission apparatus outputs a shifted torque through a planet carrier rotatably supporting the plurality of first pinion gears and a plurality of second pinion gears of the first planetary gear set.