An apparatus and method for driving a liquid crystal display device are disclosed in which the response speed of the liquid crystal can be increased without using a digital memory. The driving apparatus includes a liquid crystal panel with gate lines and data lines arranged perpendicularly to each other, a gate driver that supplies a gate pulse to the gate lines, and a data driver. The data driver samples an input N-bit digital data signal to generate an analog data voltage, generates a modulated data voltage for acceleration of a response speed of the liquid crystal according to an M-bit data value of the sampled digital data signal, mixes the modulated data voltage with the analog data voltage, and supplies the mixed data voltage to the data lines.