A stereoscopic image display apparatus and a driving method of the display apparatus are provided. The display apparatus includes a resolution enhancer that calculates an average brightness of first left-eye image data included in an nth (n is a natural number) line of the 3D image data and second left-eye image data included in an n+2th line of the 3D image data to obtain left-eye average data, calculates an average brightness of first right-eye image data included in an n+1th line of the 3D image data and second right-eye image data included in an n+4th line of the 3D image data to obtain right-eye average data, and converts the brightness of the left-eye average data and the right-eye average data into grayscale values.