Disclosed is an LCD and driving method thereof. The present invention comprises a data gray signal modifier for receiving gray signals from a data gray signal source, and outputting modification gray signals by consideration of gray signals of present and previous frames; a data driver for changing the modification gray signals into corresponding data voltages and outputting image signals; a gate driver for sequentially supplying scanning signals; and an LCD panel comprising a plurality of gate lines for transmitting the scanning signals; a plurality of data lines, being insulated from the gate lines and crossing them, for transmitting the image signals; and a plurality of pixels, formed by an area surrounded by the gate lines and data lines and arranged as a matrix pattern, having switching elements connected to the gate lines and data lines.