There is provided a vehicle-power-generator control apparatus and the control method thereof that does not notify a passenger of any erroneous alarm indicating an abnormality in an electric power generator, even when a power-generation stop command is received. it is determined that a vehicle power generator is not rotating, when the rotation speed, of the vehicle power generator, that is detected based on a power-generation voltage generated across an armature winding of the vehicle power generator is the same as or lower than a predetermined value; there is generated a power-generation stop holding signal obtained by delaying by a predetermined time a time point at which a power-generation stop signal, generated when the decoded command signal is a power-generation stop command signal for stopping electric-power generation, stops; then, the non-rotation determination signal is masked and invalidated, based on the power-generation stop holding signal.