Discussed are an apparatus and method for driving a liquid crystal display device, whereby the apparatus includes a data driver for driving data lines of a liquid crystal panel, setting detectable temperatures for different temperature detection time points, detecting an ambient temperature at each temperature detection time point, and outputting a gate drive voltage variation signal and a common voltage variation signal in accordance with the set and detected temperatures at each temperature detection time point, and a power supplier for varying levels of a gate drive voltage and a common voltage in accordance with the gate drive voltage variation signal and the common voltage variation signal, and supplying the gate drive voltage and common voltage to a gate driver and the liquid crystal panel, respectively.