A stereoscopic image display and a method for driving the same are disclosed. The stereoscopic image display includes a display panel displaying a two-dimensional (2D) image data in a 2D mode and displaying a three-dimensional (3D) image data in a 3D mode, a gamma reference voltage generating circuit that generates first gamma reference voltages and second gamma reference voltages different from the first gamma reference voltages, outputs the first gamma reference voltages in the 2D mode, and outputs the second gamma reference voltages in the 3D mode, and data driver that converts the 2D image data into the first gamma reference voltages in the 2D mode and converts left eye image data and right eye image data into the second gamma reference voltages in the 3D mode.