A liquid crystal display and a method of driving the same capable of improving contrast properties by implementing a local dimming method and achieving the slimness of the liquid crystal display are provided. The liquid crystal display includes a liquid crystal display panel which displays a picture; a backlight unit including a light guide plate part in which first light guide channels of a first direction and second light guide channels of a second direction intersected with the first direction are formed, first light array for illuminating light to the first light guide channels, and second light array for illuminating light to the second light guide channels, respectively, wherein blocks are defined by the intersection of the first light guide channels and second light guide channels; and a dimming controller for analyzing an input picture to correspond to the blocks to obtain first dimming values for independently controlling luminances of light sources of the first light array, determining second dimming values for independently controlling luminances of light sources of the second light array based on the first dimming values, and adjusting the first and second dimming values so that a luminance difference between neighboring blocks caused by the first and second dimming values is decreased.