An organic light emitting diode (OLED) display device and a method for driving the same, are capable of achieving an enhancement in response characteristics of OLEDs and an enhancement in display picture quality through application of an overdriving (or accelerated driving) method taking into consideration intrinsic response characteristics of OLEDs. The OLED display device includes an image display panel including a plurality of pixel regions, and a driving integrated circuit for converting digital image data into an analog image signal, generating a plurality of gamma voltage levels through modulation, for overdriving or accelerated driving of the analog image signal, and modulating gray levels of the digital image data such that the modulated gray levels correspond to the modulated gamma voltage levels, for display of an image according to the modulated image data on the image display panel.