The present invention provides a grey-scale LCD driver which can realize multi-gradation by varying a voltage applied to a liquid crystal layer. The grey-scale LCD driver includes a data storing section for storing n bits of digital data assigned for producing a grey scale; a counter for generating counting data; a comparator for comparing the digital data stored in the data storing section with the counting data outputted from the counter and outputting a comparing signal if the digital data is equal to the counting data to control a sampling switching means; a rectangular-waveform voltage generating means for generating a rectangular-waveform voltage signal applied to the sampling switching means as a driving voltage; an integrating circuit for shaping a rectangular-waveform voltage supplied through the switching means into a ramp voltage, the integrating circuit being composed of a liquid crystal capacitor and a resistor; and a discharging switch means for discharging charges accumulated in the liquid crystal capacitor according to a control signal of a controller.