An inverter control apparatus comprising: an inverter main circuit that drives a synchronous motor with magnetic saliency; an electric-current detector that detects an electric current flowing between the inverter main circuit and the synchronous motor; a command generator that generates an electric-current command value of an output electric current that is output from the inverter main circuit to the synchronous motor, in accordance with a torque command (T*) that is supplied externally; and an electric-current controller that generates a voltage command value for the inverter main circuit so that the electric-current command value and a detected electric-current value detected in the electric-current detector are equal to each other, wherein the electric-current command value includes a d-axis electric-current command value (I dref) and a q-axis electric-current command value (I qref), the command generator comprises an electric-current command generator configured to generate a first d-axis electric-current command value (I d1 *) according to the torque command and a limiting unit that sets, when an absolute value of the d-axis electric-current command value is smaller than a lower limit value, the absolute value of the d-axis electric-current command value to a value which is equal to the lower limit value, so that a fundamental wave current, an absolute value of an amplitude of which is equal to or greater than the lower limit, is supplied to the synchronous motor to saturate a rotor bridge unit of the synchronous motor magnetically, in driving the inverter main circuit; characterised in that the limiting unit is configured to output an absolute value of a second d-axis electric-current command (I d2 *) which is equal to an absolute value of the first d-axis electric-current command when an absolute value of the first d-axis electric-current command is equal to or greater than the lower limit and output an absolute value of the second d-axis electric-current command which is equal to the lower limit when an absolute value of an amplitude of the first d-axis electric-current command is smaller than the lower limit; an electric-current corrector which receives the second d-axis electric-current command value from the limiting unit and a q-axis inductance value, and which calculates the q-axis electric-current command value, and a q-axis inductance corrector which receives the q-axis electric-current command value calculated in the electric-current corrector, corrects the q-axis inductance value, and outputs the corrected q-axis inductance value to the electric-current corrector. an inverter main circuit that drives a synchronous motor with magnetic saliency; an electric-current detector that detects an electric current flowing between the inverter main circuit and the synchronous motor; a command generator that generates an electric-current command value of an output electric current that is output from the inverter main circuit to the synchronous motor, in accordance with a torque command (T*) that is supplied externally; and an electric-current controller that generates a voltage command value for the inverter main circuit so that the electric-current command value and a detected electric-current value detected in the electric-current detector are equal to each other, wherein the electric-current command value includes a d-axis electric-current command value (I dref) and a q-axis electric-current command value (I qref), the command generator comprises an electric-current command generator configured to generate a first d-axis electric-current command value (I d1 *) according to the torque command and a limiting unit that sets, when an absolute value of the d-axis electric-current command value is smaller than a lower limit value, the absolute value of the d-axis electric-current command value to a value which is equal to the lower limit value, so that a fundamental wave current, an absolute value of an amplitude of which is equal to or greater than the lower limit, is supplied to the synchronous motor to saturate a rotor bridge unit of the synchronous motor magnetically, in driving the inverter main circuit; characterised in that the limiting unit is configured to output an absolute value of a second d-axis electric-current command (I d2 *) which is equal to an absolute value of the first d-axis electric-current command when an absolute value of the first d-axis electric-current command is equal to or greater than the lower limit and output an absolute value of the second d-axis electric-current command which is equal to the lower limit when an absolute value of an amplitude of the first d-axis electric-current command is smaller than the lower limit; an electric-current corrector which receives the second d-axis electric-current command value from the limiting unit and a q-axis inductance value, and which calculates the q-axis electric-current command value, and a q-axis inductance corrector which receives the q-axis electric-current command value calculated in the electric-current corrector, corrects the q-axis inductance value, and outputs the corrected q-axis inductance value to the electric-current corrector.