An inverter control apparatus and a motor drive system includes an inverter main circuit that drives a synchronous motor; 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 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. The command generator generates the electric-current command value so that a fundamental wave current that is equal to or greater than a threshold is supplied to the synchronous motor, in driving the inverter main circuit.