An apparatus for driving a liquid crystal display (LCD) device includes a liquid crystal panel including 4-color sub-pixels, a data driver to provide video data signals to each sub-pixel, a gate driver to provide a scan pulse to each sub-pixel, a data conversion part to generate a gain value by analyzing a ratio of an achromatic color signal to a chromatic color signal of 3-color source data inputted from an external source and convert the 3-color source data into 4-color data using the generated gain value, and a timing controller to provide the 4-color data received from the data conversion part to the data driver and control the gate driver and the data driver.