Lead thin film capacitors with high energy storage performance have attracted increasing interest in their applications in modern devices. In this study, the energy storage performances of Pb0.95La0.02(Zr0.5Sn0.5)O3 antiferroelectric thin films were enhanced by incorporating Al2O3 and HfO2 buffer layers. The electrical properties and energy storage characteristics of antiferroelectric thin films with different buffer layers were analyzed to study the impact of buffer layers on energy storage performance. After the incorporation of Al2O3 and HfO2 buffer layers, the breakdown field strength (Eb) of the films were significantly increased and the leakage current densities were greatly reduced with the ohmic conduction range widened at low electric fields. As a result, the energy storage density of films with Al2O3 and HfO2 buffer layers increased significantly from 10.07 to 31.54 and 22.63 J/cm3, respectively. By analyzing the leakage current, it was found that the Poole–Frenkel emission was significantly suppressed by the Al2O3 buffer layer, while the HfO2 buffer layer had a limited effect on the conduction mechanisms, which resulted in the better energy storage performance of those films with Al2O3 buffer layers. The results demonstrate that the improvement of energy storage performance is attributed to the leakage current emission mechanism affected by the buffer layer.