A motor driving apparatus comprising: an inverter to convert DC voltage into AC voltage and to output the AC voltage to the motor; and an inverter controller to control the inverter during a starting operation of the motor, wherein the inverter controller is configured to: supply a constant current (i da) to the motor so as to align a rotor of the motor during a starting operation time period; and, supply a torque current (i oa) for rotating the motor during a normal operation time period; when the starting operation of the motor is completed, stop supplying the constant current (i da) to the motor, wherein the constant current (i da) includes a d-axis current having a constant value and a q-axis current having a zero value, wherein the inverter controller is configured to control the inverter to partially overlap a time period for supplying the constant current (i da) and a time period for supplying the torque current (i oa) to each other, and wherein the inverter controller is configured to control the inverter to gradually increase the torque current (i oa) and supply the constant current (i da) to the motor during the normal operation time period including an overlapping time period (T ov) for supplying the constant current (i da) and the torque current (i oa). an inverter to convert DC voltage into AC voltage and to output the AC voltage to the motor; and an inverter controller to control the inverter during a starting operation of the motor, wherein the inverter controller is configured to: supply a constant current (i da) to the motor so as to align a rotor of the motor during a starting operation time period; and, supply a torque current (i oa) for rotating the motor during a normal operation time period; when the starting operation of the motor is completed, stop supplying the constant current (i da) to the motor, wherein the constant current (i da) includes a d-axis current having a constant value and a q-axis current having a zero value, wherein the inverter controller is configured to control the inverter to partially overlap a time period for supplying the constant current (i da) and a time period for supplying the torque current (i oa) to each other, and wherein the inverter controller is configured to control the inverter to gradually increase the torque current (i oa) and supply the constant current (i da) to the motor during the normal operation time period including an overlapping time period (T ov) for supplying the constant current (i da) and the torque current (i oa). supply a constant current (i da) to the motor so as to align a rotor of the motor during a starting operation time period; and, supply a torque current (i oa) for rotating the motor during a normal operation time period; when the starting operation of the motor is completed, stop supplying the constant current (i da) to the motor, wherein the constant current (i da) includes a d-axis current having a constant value and a q-axis current having a zero value, wherein the inverter controller is configured to control the inverter to partially overlap a time period for supplying the constant current (i da) and a time period for supplying the torque current (i oa) to each other, and wherein the inverter controller is configured to control the inverter to gradually increase the torque current (i oa) and supply the constant current (i da) to the motor during the normal operation time period including an overlapping time period (T ov) for supplying the constant current (i da) and the torque current (i oa).