A motor control apparatus comprising: an inverter configured to apply a voltage to an AC induction motor to be driven; a command value calculator (13, 18) configured to calculate a command value of an AC voltage outputted from the inverter on the basis of a target motor torque of the AC induction motor; and an inverter controller (15, 16, 12, 6) configured to control the inverter on the basis of the command value of the AC voltage, characterized in that the target motor torque of the AC induction motor includes a first target motor torque and a second target motor torque, a high speed response being required in the first target motor torque, which is used for suppressing torsional vibration, the second target motor torque being a lower speed response than the first target motor torque, time delay processing being carried out by a filter for the second target motor torque so that the second target motor torque output by the filter is delayed at least for a period of time longer than a response time of the second target motor torque that is defined in accordance with an accelerator opening degree, wherein the command value calculator (13, 18) is configured to calculate, on the basis of the target motor torque, a magnetic flux current command value, and the command value calculator (13, 18) is configured to calculate, on the basis of the target motor torque and the magnetic flux current command value, a torque current command value, wherein the magnetic flux current command value and the torque current command value are obtained by converting a three-phase AC current into an orthogonal biaxial coordinate system synchronized with a power source angular frequency, and wherein current responsiveness of the torque current value to torque current command value is quicker than that of the magnetic flux current value to the magnetic flux current command value. an inverter configured to apply a voltage to an AC induction motor to be driven; a command value calculator (13, 18) configured to calculate a command value of an AC voltage outputted from the inverter on the basis of a target motor torque of the AC induction motor; and an inverter controller (15, 16, 12, 6) configured to control the inverter on the basis of the command value of the AC voltage, characterized in that the target motor torque of the AC induction motor includes a first target motor torque and a second target motor torque, a high speed response being required in the first target motor torque, which is used for suppressing torsional vibration, the second target motor torque being a lower speed response than the first target motor torque, time delay processing being carried out by a filter for the second target motor torque so that the second target motor torque output by the filter is delayed at least for a period of time longer than a response time of the second target motor torque that is defined in accordance with an accelerator opening degree, wherein the command value calculator (13, 18) is configured to calculate, on the basis of the target motor torque, a magnetic flux current command value, and the command value calculator (13, 18) is configured to calculate, on the basis of the target motor torque and the magnetic flux current command value, a torque current command value, wherein the magnetic flux current command value and the torque current command value are obtained by converting a three-phase AC current into an orthogonal biaxial coordinate system synchronized with a power source angular frequency, and wherein current responsiveness of the torque current value to torque current command value is quicker than that of the magnetic flux current value to the magnetic flux current command value.