An apparatus for controlling a head up display of a vehicle includes a navigation device that calculates a residual distance from a position of the vehicle to a driving direction change point, a display that displays vehicle information as an augmented reality image, and a controller that compares the residual distance with a preset distance, determines whether to correct the residual distance depending on a result of the comparison, corrects the residual distance based on an output height of the augmented reality image when correcting the residual distance, and sets a position spaced apart by the corrected residual distance from the position of the vehicle as a projected position of the augmented reality image.