1. A gesture recognition apparatus for a vehicle, comprising: a storage unit to store a vein pattern lookup table including a plurality of reference vein pattern images according to a rotation angle of a driver's hand; an image acquisition unit to acquire a driver's image comprising an image of the driver's hand; and a controller to: extract a vein pattern image of the driver's hand from the driver's image; authenticate the driver by comparing the extracted vein pattern image with the vein pattern lookup table; and determine a gesture of the driver comprising at least one of a position of the driver's hand, a direction directed by the driver's hand and the rotation angle of the driver's hand based on the extracted vein pattern image, wherein the controller searches for a reference vein pattern image matched to the extracted vein pattern image among the plurality of reference vein pattern images and determines the rotation angle of the driver's hand based on the reference vein pattern image matched to the extracted vein pattern image.