1. A motor control apparatus for controlling rotation of a three-phase AC motor by determining a switching mode of an inverter so that a current flowing through the three-phase AC motor becomes equal to a command current, whereby the inverter operates in the determined switching mode so that a voltage corresponding to the switching mode is applied to the three-phase AC motor, the motor control apparatus comprising: a zero vector current calculator that calculates a prediction current as a zero vector current, the prediction current being predicted to flow through the three-phase AC motor when the inverter operates in a zero vector switching mode for applying no voltage to the three-phase AC motor; a determinator that determines whether a difference between the zero vector current and the command current on a αβ stationary coordinate system falls within an allowable range, the αβ stationary coordinate system having an origin at a rotation axis of a rotor of the three-phase AC motor and defined by a α-axis and a β-axis which are perpendicular to each other; and a selector that selects the zero vector switching mode as the switching mode of the inverter upon determination that the difference between the zero vector current and the command current falls within the allowable range, the selector selecting a non-zero vector switching mode as the switching mode of the inverter upon determination that the difference between the zero vector current and the command current falls outside the allowable range, the non-zero vector switching mode corresponding to a non-zero current vector closest to the command current among six non-zero current vectors defined in fixed directions with respect to the zero vector current on the αβ stationary coordinate system.