Poly(vinylidene fluoride) (PVDF) based polymer/ceramic nanocomposites for high energy density dielectrics have long been plagued by their low discharging efficiency (40-60%), which originates from the matrix with high bulk ferroelectric relaxation and the high-k ceramics with large conduction loss. In this work, a linear-like PVDF-based polymer dielectric is synthesized through grafting poly(methyl methacrylate) (PMMA) onto main chains of poly(vinyl fluoride-trifluoroethylene-chlorotrifluoroethylene) (P(VDF-TrFE-CTFE)) terpolymer via an atom transfer radical polymerization (ATRP) process. PMMA grafted terpolymer (P(VDF-TrFE-CTFE)-g-PMMA) shows linear-like dielectric characteristics accompanied with greatly enhanced discharging efficiency of similar to 80% under 250 MV/m, which is over 100% higher than that of pristine terpolymer. To further improve its breakdown strength and discharging efficiency, the grafted terpolymer are then compounded with ultrasonic-exfoliated mica nanosheets (eMica) by solution-cast method. Thanks to the low hysteresis loss of linear-like dielectric matrix and the high insulating 2D mica nanosheets, the composite with the highest discharging efficiency of similar to 78% under 250 MV/m is achieved. The maximum energy density of the optimized composite reaches 9.6 J/ cm(3), which is nearly 290% that of the pristine terpolymer. Besides, its discharging efficiency is about 74% under 450 MV/m, which is much more advantageous than the other PVDF-based polymer/ceramics composite dielectrics. This work suggests that utilizing polymer matrix with linear dielectric property and fillers with high insulating 2D structure might be a facile strategy to achieve composite dielectrics with simultaneously high energy density and high discharging efficiency.