Flexible antiferroelectric (AFE) Pb0.94La0.04Zr0.97Ti0.03O3 (PLZT) thick-film capacitors were fabricated on nickel foil substrates using sol-gel method. The thick PLZT film shows pure perovskite phase with dense microstructure. The discharge energy-storage properties of the thick PLZT film are directly evaluated by the resistance-inductance-capacitance (RLC) circuit. The maximum value of the discharge energy-storage density (W-dis) is 15.8 J/cm(3) at 1400 kV/cm and 90% of the corresponding energy is released in a short time of about 250 ns. In addition, the W-dis and discharge time could be adjusted by the bent radius of the film, which provides a simple and feasible solution for the regulation of the electrical performance. Furthermore, the flexible AFE film exhibits good mechanical properties under cycling tests with bending radii down to 2.5 mm and 1500 rounds. This work shows a critical significance in fabricating flexible AFE capacitors for application in modern electronics and electrical power systems.