An electric drive apparatus comprising: an electric motor adapted to drive a driven member; an inverter to supply an electric power from a power source to the motor; a continuously-variable transmission connected with the motor, to transmit rotation from the motor to the driven member; and a controller to control the motor by controlling the inverter and to control a transmission ratio of the continuously-variable transmission, to achieve a desired driving torque, characterized by the controller being configured, to determine whether a demand motor operation point determined by a demand motor speed (Nd) and a demand motor torque (Td) is within a predetermined motor operation range in which the demand motor speed is within a predetermined speed range, and the demand motor torque is within a predetermined torque range, the demand motor torque being a torque determined from the desired driving torque and the demand motor speed being a speed determined from a speed of the driven member on the assumption that the transmission ratio of the continuously-variable transmission is equal to a predetermined assumed ratio; to control 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 the demand motor operation point is within the predetermined operation range; and to control the motor and the continuously-variable transmission in a second control mode to vary the transmission ratio of the continuously-variable transmission and to control the motor to achieve the desired driving torque when the demand motor operation point is not within the predetermined operation range. an electric motor adapted to drive a driven member; an inverter to supply an electric power from a power source to the motor; a continuously-variable transmission connected with the motor, to transmit rotation from the motor to the driven member; and a controller to control the motor by controlling the inverter and to control a transmission ratio of the continuously-variable transmission, to achieve a desired driving torque, characterized by the controller being configured, to determine whether a demand motor operation point determined by a demand motor speed (Nd) and a demand motor torque (Td) is within a predetermined motor operation range in which the demand motor speed is within a predetermined speed range, and the demand motor torque is within a predetermined torque range, the demand motor torque being a torque determined from the desired driving torque and the demand motor speed being a speed determined from a speed of the driven member on the assumption that the transmission ratio of the continuously-variable transmission is equal to a predetermined assumed ratio; to control 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 the demand motor operation point is within the predetermined operation range; and to control the motor and the continuously-variable transmission in a second control mode to vary the transmission ratio of the continuously-variable transmission and to control the motor to achieve the desired driving torque when the demand motor operation point is not within the predetermined operation range.