The dielectric behaviour of antiferroelectric lead zirconate titanate has been studied by measuring the polarization and capacitance changes with the electric field.The results show that the differential dielectric constant　εd calculated from the polarization versus electric field curve exhibits sharp peaks at the electric fields that switch an antiferroelectricsferroelectrics transition,and the maximum value of εd can reach up to 41000. The smallsignal dielectric constant εc measured will decrease rapidly during the phase transition from an antiferroelectric state to a polarized ferroelectric state by increasing the dc bias field, and εc　will increase during the ferroelectric state returns to the original antiferroelectric state by reducing dc bias field. It is noticed that the extreme values of the differential dielectric constant εd are electric hysteretic to the extreme of the small signal dielectric constant εc. These phenomena are analyzed by using the electric domain evolution under an electric field.