1. A motor control device that determines a switching mode of an inverter so that a current flowing in a three-phase AC motor matches a command current, allows the inverter to operate in the switching mode that is determined, and applies a voltage corresponding to the switching mode to the three-phase AC motor to control the rotation of the three-phase AC motor, the motor control device comprising: a zero vector current arithmetic portion calculating a current predicted to flow in the three-phase AC motor as a zero-vector current when the inverter operates in a zero vector switching mode in which no voltage is applied to the three-phase AC motor; a current vector selection portion selecting a current vector closest to the command current among current vectors flowing in the three-phase AC motor which are set in directions fixed relative to the zero vector current when the inverter operates in six non-zero vector switching modes where a voltage is applied to the three-phase AC motor, in an αβ static coordinate system which is defined by an α-axis and a (β-axis orthogonal to each other with a rotation axis of a rotor of the three-phase AC motor as an origin; a non-zero vector current arithmetic portion calculating a current predicted to flow in the three-phase AC motor as the non-zero vector current when the inverter operates in the non-zero vector switching modes corresponding to the current vector selected by the current vector selection portion; and a current selection portion selecting a current close to the command current from the zero vector current and the non-zero vector current, wherein the switching mode corresponding to the current selected by the current selection portion is determined as the switching mode of the inverter.