A liquid crystal display device and a driving method thereof for preventing a brightness difference between horizontal line blocks are disclosed. In the liquid crystal display device, a liquid crystal display panel has a liquid crystal cell matrix. A power supply generates a common voltage. Common lines directly on a substrate of the liquid crystal display panel are connected to a common electrode of the liquid crystal cell. A common voltage compensator compensates for the common voltage into a large resistance value with a resistance value greater than a combination of resistances of the common lines and the large resistance directly between the power supply and the common lines.