A liquid crystal display and a driving method thereof capable of improving contrast properties by implementing a local dimming and achieving the slimness of the liquid crystal display. The liquid crystal display comprises a liquid crystal display panel, a backlight unit including a light guide plate part in which a plurality of light guide channels are formed, and a plurality of light sources for illuminating light to the light guide channels, a division driving controller for mapping an input picture to a plurality of blocks in which a plurality of data channels are intersected with the plurality of light guide channels, analyzing luminance of the input picture for each block, determining dimming values of the plurality of light sources, and independently modulating the luminance of the input picture for each block based on the analyzed result, and a light source driver for independently controlling luminance of the light sources responding to the dimming values.