Polymer dielectrics are extensively studied for applications in electronics pulsed power systems owing to their excellent processability, high breakdown strength and low energy loss. To synergistically achieve high energy density and high discharge efficiency, we report an asymmetric three-layer all-polymer composite, which consists of a mixture of P(VDF-HFP) and P(St-MMA) as an intermediate layer sandwiched between a linear polymer P(St-MMA) dielectric layer and a nonlinear polymer P(VDF-HFP) dielectric layer. The results of the study showed that a high efficiency of 94.14 % and a high energy discharge density of 14.86 J/cm3 were achieved concurrently. In this case, the linear dielectric layer provides high energy efficiency, and the high energy density is provided by the nonlinear layer dielectric layer. In particular, the middle layer can effectively balance the electric field distribution, which improves the breakdown strength and increases the energy density. The structural design of asymmetric three-layer all-polymer films provides an effective way to realize high-performance dielectric energy storage materials.