A display device including a liquid crystal display unit and a controller displays an image using a liquid crystal. The controller extracts a compensation data from a gray compensation look-up table (LUT) corresponding to a temperature interval including a peripheral temperature of the display device to output the compensation data to the liquid crystal display unit as a compensated gray data. When the gray compensation LUT does not exist, the controller extracts the compensation data from the gray compensation LUT corresponding to the temperature interval approximating the peripheral temperature to generate the compensated gray data. The gray compensation LUT as a default and a calculated gray compensation LUT may be used to provide the compensated gray data optimized for the response speed of the liquid crystal according to variance in temperature, while reducing a memory capacity of a ROM and a RAM inside the timing controller and an external EEPROM.