A light source module having a plurality of light source blocks corresponding to a plurality of display regions, a method for driving the light source module, and a display device having the light source module. The output brightness of each of the light source blocks is individually dimmed according to a dimming control signal. A dimming control unit determines the average gray level and inherent brightness of each of the respective display regions, calculates a threshold gray level of each display region by using its inherent brightness, outputs a fixed brightness as a dimming control signal when the average gray level of the display region is greater than the threshold gray level, and outputs a variable brightness based upon the inherent brightness value, as the dimming control signal when the average gray level of the display region is less than the threshold gray level.