A display device including a touch sensor and a driving method thereof, and more particularly, a curved display device including a touch sensor and a driving method thereof, are presented. The display device includes: a touch sensor unit including a plurality of touch sensors; and at least one touch surface curved to along a first direction, wherein the touch surface includes a center region and edge regions positioned at both sides of the center region along the first direction, and wherein a sensitivity of the touch sensor in the center region is higher than a sensitivity of the touch sensors in the edge regions.