A display device and driving method thereof are disclosed. The display device includes a pixel emitting light at a luminance corresponding to an output grayscale value and a color shifter for converting an input grayscale value into the output grayscale value based on output color gamut information. The color shifter includes an offset storage unit storing reference color gamut information and offset information; and a color gamut determination unit that determines the output color gamut information using the reference color gamut information and the offset information when the color shift level corresponds to a value between the reference level and the shift levels, and determines tire output color gamut information using second offset information in which the offset information is inverted and the reference color gamut information when the color shift level is not between the reference level and the shift levels.