We propose the unique structure of highly dispersible single-walled carbon nanotubes (SWCNTs) in various solvents and polymers using the ZnO nano particle template. Buckled nanospring-shaped carbon nanotubes (NS-CNTs) were synthesized by a chemical reaction of ZnO nanoparticles with acid-treated SWCNTs and then dissolving ZnO through chemical etching. The unique structure of distorted hexagonal NS-CNTs encircled around ZnO nanoparticles was formed by the bending of SWCNTs caused by the agglomeration of chemically adsorbed Zn(OH)2, which is further crystallized as the polycrystalline ZnO inner core. The highly dispersible NS-CNTs could be incorporated in the poly[(vinylidenefluoride-co-trifluoroethylene] [P(VDF-TrFE)] copolymer, one of widely studied ferro- and piezo-electric polymer, up to the value of 15 wt% as nanofillers. The relative dielectric constant (K) of polymer nanocomposite, at 1 kHz, was greatly enhanced from 12.7 to the value of 62.5 at 11 wt% of NS-CNTs, corresponding to a 492% increase compared to that of pristine P(VDF-TrFE) with only a small dielectric loss tangent (D) of 0.1.