A liquid crystal display and a method for driving the same are disclosed. The liquid crystal display includes a display panel which is virtually divided into a plurality of blocks, a backlight unit including a plurality of light sources irradiating light onto the display panel, a backlight dimming controller which analyzes digital video data, calculates a dimming value of each of the blocks, and adjusts a global dimming value based on the dimming values of the blocks so as to increase brightness of the plurality of light sources within previously determined power consumption, and a light source driver which outputs light source driving signals for driving the plurality of light sources based on the dimming values of the blocks and the global dimming value.