PURPOSE: A liquid crystal display and a driving method thereof are provided to minimize vertical strain strip by using a demultiplex circuit of an amorphous silicon. CONSTITUTION: In a liquid crystal display and a driving method thereof, a plurality of data lines receive data voltage from a plurality of output channels. A first control signal bus line receives a first control signal. A second control signal bus line receives a second control signal later than the first control signal. A first switching device switches a current path between an output channel and the first data lines in response to the first control signal. A demultiplex circuit switches a current path between the output channel and the second data liens in response to the second control signal.