A mobile display device driving apparatus and method which can reduce power consumption are disclosed. The driving apparatus includes a liquid crystal panel having a plurality of liquid crystal cells each formed in sub-pixel areas of four colors, a battery charged with a voltage, a power saving mode signal generator that detects the remaining power of the battery and generates a power saving mode signal based on the detected power to set a power saving mode of the liquid crystal panel. A controller sets a gain value in response to the power saving mode signal, converts external three-color input data into four-color data based on the set gain value and generates a dimming signal in response to the power saving mode signal. A panel driver displays an image based on the four-color data on the liquid crystal panel. An inverter generates a lamp drive voltage based on the dimming signal, and a backlight unit generates light in response to the lamp drive voltage and irradiates the generated light to the liquid crystal panel.