Metallized film capacitors use plastic films as the dielectric spacer, and these polymer films generally have low dielectric constants. To boost the electrostatic energy storage density of a film capacitor, advanced high-k films with high electrical breakdown strength and low dielectric loss are highly desired. Herein, polymer nanocomposite films were made by filling ZnO@CuO nanosheets into poly(vinylidene fluoride-co-hexafluoropropylene) [P(VDF-HFP)]. The n-type ZnO nanosheets are synthesized in an aqueous solution. Through a calcination process, thin layers of p-type CuO are coated over the ZnO nanosheets. Compared to pure P(VDF-HFP) and ZnO/P(VDF-HFP) films, the ZnO@CuO/P(VDF-HFP) films exhibit higher dielectric constant and higher breakdown strength. The optimal content of ZnO@CuO nanosheet in the polymer matrix is determined to be 3 wt%, which leads to a dielectric constant of 15.6 at 1 kHz and the highest energy density of 5.6 J cm-3. The efficacy of ZnO@CuO nanosheets in enhancing the dielectric performance of the polymer nanocomposite is elucidated in detail. This research provides a scalable and low-cost strategy to produce polymer nanocomposite films with high capacitive energy storage performance.