An apparatus and method of driving a liquid crystal display device are disclosed in the present invention. The liquid crystal display device includes a plurality of data lines in a first direction, a plurality of gate lines in a second direction to cross the data lines, a plurality of first liquid crystal cells on a first side with respect to the data lines, a plurality of second liquid crystal cells on a second side with respect to the data lines, a first switching part in each first liquid crystal cell and controlled by a current gate line and a next gate line, and a second switching part in each second liquid crystal cell and controlled by the current gate line and a previous gate line.