Based on the investigation of mechanism for large dielectric losses in relaxor fluorinated polymers, polyvinylidene fluoride (PVDF) derivatives, a new nanostructure-controlled PVDF based polymer films with low dielectric toss. tanδ < 1% (0.6%). and high dielectric constant, εr = 13 at frequency of 1 kHz, was proposed for electrical energy storage applications. The high dielectric loss was mainly due to the electric-field induced α-β phase transition, and one dimensional extension of P(VDF-TrFE)-g-PEMA films was found to reduce the α phase component resulting in reduction of the dielectric loss while keeping the high dielectric constant. In-situ FTIR measurements suggested a possibility of further reducing the dielectric-loss.