The AC motor driving apparatus comprises an inverter for supplying power to an AC motor, current sensors for detecting current that flows in the motor or inverter, a rotation sensor for detecting the rotation of the rotor in the motor, and a control unit for controlling the driving of the inverter. A current detection value detected by the current sensor and a rotor rotational position are used to estimate three-phase motor current values. The estimated motor current values are used to control the inverter. Thereby, an inexpensive, space-saving AC motor driving apparatus as well as an AC motor controller, electric actuator, or vehicle that can perform highly precise torque control from zero speed to high-speed rotation without depending on the PWM pulse pattern are provided.