A liquid crystal display driven by a dot-line inversion driving method in combination with a 2-step dot sequential precharge driving method which, if black window or black lines are displayed, is free of horizontal trails on circumscribing portions thereof is provided. Before video signals having opposite polarities are applied to signal lines, first, a full-line precharge pulse is generated in the horizontal blanking periods, and precharge gray signals which have the same polarity as that of the previous pixel potential are written together based on the full-line precharge pulse. Then, precharge black signals having the same polarity as that of one of the video signals and precharge gray signals having the same polarity of that of the other video signal are written in two steps.