A method and an apparatus for driving passive matrix liquid crystal, comprising the steps of: simultaneously selecting Y row electrodes, where Y is an odd number of 7 and above; calculating an exclusive OR between a Y-bit row selection vector representing a selection pattern of the Y row electrodes and Y-bit ON/OFF display data representing a display pattern of column electrodes, for each corresponding bit; adding the exclusive ORs for each bit; when X=(Y+1)/2, and a 1/(X-1) voltage of the maximum voltage of the column electrodes is Vc, selecting a voltage level of the column electrodes from X voltage levels satisfying: [2.times.i-(X-1)].times.Vc (i=an integer of 0 to (X-1)) in accordance with the result of the addition for driving. These method and apparatus prevent the frame response phenomenon of high-speed liquid crystal while realizing high-contrast display, low-voltage driving, low power consumption, and reduction in chip size.