The present invention provides a method for driving a liquid crystal display panel and a liquid crystal display so that the power consumption for driving a 3D liquid crystal display panel can be reduced. The method includes steps of: determining that it is needed to input data to the black matrix sub-pixels when displaying a 3D image; and inputting a control signal to a 3D black screen data control module, the 3D black screen data control module, based on the received control signal, makes two data lines which are connected therewith and are of opposite polarities be electrically conducted.