Achieving higher dielectric constant (Dk) at lower conductor content is an interesting challenge for developing high-Dk composites. Herein, novel 3D-framework (fPCNT) from polyvinylidene fluoride (PVDF) and carbon nanotubes (CNTs) was prepared, which was infiltrated with epoxy (EP) resin to fabricate new composites (fPCNT/EP). The crystalline phase, spatial distribution and interfacial interaction of fPCNT were discussed, and dielectric properties of fPCNT/EP were compared with those of traditional filler embedded composites (CNT/EP and CNT/PVDF/EP) and four composites (M450-CNT/EP, M20-CNT/EP, CNa-CNT/EP and CC-CNT/EP) based on 3D-frameworks from CNTs and traditional cellulose binders. fPCNT/EP not only has much lower percolation threshold (fc = 0.25 wt%) and higher Dk at fc (170, 100 Hz) than CNT/EP and CNT/PVDF/EP, but also shows higher Dk and better Dk-frequency stability than M450-CNT/EP, M20-CNT/EP, CNa-CNT/EP and CC-CNT/EP composites with same CNT contents. The mechanism behind was intensively investigated through building structure-property relationship.