An electric drive apparatus includes a controller for controlling an electric motor and a continuously-variable transmission connected with the motor. The controller controls the motor and the continuously-variable transmission in a first control mode to control the transmission ratio of the continuously-variable transmission to a predetermined fixed ratio so as to hold the transmission ratio at the fixed ratio, and to control the motor to achieve the demand motor torque when a demand motor operation point determined from a predetermined assumed ratio is within a predetermined operation range, and to control the motor and the continuously-variable transmission in a second control mode to vary the transmission ratio and to control the motor to achieve a desired driving torque for a driven member driven by the motor when the demand motor operation point is not within the predetermined operation range.