There is disclosed a liquid crystal display device and driving method are provided. The liquid crystal display device includes a liquid crystal display panel where pixels are defined by gate lines and data lines that are arranged in a matrix shape. A gate driver is operable to supply a gate voltage to the liquid crystal display panel. A data driver is operable to supply a data voltage to the liquid crystal display panel. The pixels are each independently operable to be driven by drive voltages, which have different polarities from each other, and include first and second liquid crystal cells which realize the same gray level.