Abstract Polymer film capacitors are widely utilized in electronics and power suppliers because of high power density and fast charge–discharge speed. Flexible polymer that tolerates the extremes of working temperature and electric field is essential for advanced energy storage systems. Here, hyperbranched polyethylene copolymer inoculated with N –hydroxyethyl maleimide (HBPE@HEPD) has been synthesized to modify boron nitride nanosheets (HEPD‐BNNSs) via non‐covalent interaction during liquid‐phase exfoliation. The conjugated double bond serves as trapping effect through the addition reaction with free radicals in HEPD‐BNNSs/polyetherimide (PEI) nanocomposite that delays the formation of electrical treeing at initial stage of breakdown. The resultant HEPD‐BNNSs/PEI film illustrates a superior energy storage capability, e.g. discharged energy density of 12.9 J cm −3 and efficiency >90% at 500 MV m −1 and room temperature are obtained in 0.5 wt.% nanocomposite, and discharged energy density of 5.8 J cm −3 under 100 °C with efficiency of 90.2% at 350 MV m −1 is achieved in current film. The prepared HEPD‐BNNSs/PEI nanocomposite also has eminent fatigue resistance at 200 MV m −1 with charge–discharge operation over 10 5 cycles. This strategy of trapping free radicals at initial stage of breakdown reveals a fresh prospect of polymer dielectrics for film capacitor.