The liquid crystal display device includes a histogram analyzer analyzing a histogram of an input image and determining the input image as being in one of a low brightness mode, a normal mode, and a high brightness mode based on the histogram analysis, a back light controller controlling a maximum brightness of a back light unit based on the mode determination, and a data modulator enlarging the histogram of the input image to modulate data of the input image. The histogram analyzer detects a most frequent value of gray scale occurring most frequently in the input image of one frame, compares the most frequent value with a predetermined low reference gray value and a predetermined high reference gray value, and determines the input image as in one of the low brightness mode, the normal mode, and the high brightness mode based on the compared result.