The present invention relates to an antiferroelectric liquid crystal display device, by which a time (namely, a ferroelectric saturation time tr) required for transition of the state of a liquid crystal, which has been in a dark state, to a saturated bright state is reduced. A method of establishing a precedent driving period in such a manner as to be precedent to a selective driving period and of obtaining a value, at which the ferroelectric saturation time tr is minimized, of a synthetic voltage from a scanning signal and a display signal in the precedent driving period. A device using the value obtained by this method. In the precedent driving period, a voltage, whose voltage value is .vertline.Vx.vertline., is applied to the liquid crystal. In a selective driving period, a voltage, which is different in polarity from the voltage value .vertline.Vx.vertline. and has a voltage value is .vertline.Vz.vertline., is applied thereto. In other periods, a voltage having a voltage value of 0 is applied thereto. A value of the voltage .vertline.Vx.vertline., at which the ferroelectric saturation time tr is minimized when changing the value of the voltage .vertline.Vx.vertline. while maintaining the voltage .vertline.Vz.vertline. at a constant value, is set as an optimum precedent driving voltage .vertline.VM.vertline..