A matrix liquid crystal display device provided with switching transistors, made of amorphous silicon thin-film for example, which are connected to each display picture element. The switching transistors are scanned with a scan pulse having width H which is set at a value greater than that is expressed by T/N, where H denotes the scan pulse width applied to row electrodes connected to each gate of the switching transistor, T denotes the total scan time and N the number of the scan lines. Concretely, the timewise width of the scan pulses is expanded or the number of applicable scan pulses is increased. The preferred embodiments relate to such a liquid crystal display driving system that can effectively minimize the decline of the voltage and the display characteristics caused by insufficient charge against the display picture element electrodes via the switching transistors. In particular, the driving method embodied by the present invention is extremely useful for driving a large-capacity X-Y matrix liquid crystal display device.