High dielectric constant (k) and excellent insulating performance together with the thickness down-scalability are essential requirements for polymer dielectrics to realize the stable operation of flexible, low-power electronics. Crosslinking has been applied frequently to the dielectric polymer matrix to enhance the insulating performance. However, the addition of crosslinker into the polymer has been often accompanied by the reduction of the dielectric constant thereof. Herein, a series of copolymer dielectrics is synthesized composed of two monomers of 2-cyanoethyl acrylate (CEA) possessing a highly polar cyanide functional group and 1,4-butanediol divinyl ether (BDDVE), a crosslinker with relatively short chain length. The chemical composition of the 30-nm-thick copolymer dielectrics is optimized to achieve extremely low leakage current (<3.0 x 10(-8)A cm(-2)in the range of +/- 2 MV cm(-1)) with unprecedentedly high dielectric constant of 7.5, which is, to the knowledge, the highest dielectric constant among the sub-50 nm polymer dielectrics without inorganic component, reported to date. Exploiting the copolymer dielectric layers, high-performance, low-power organic thin-film transistors (OTFTs) with high operational stability and extreme mechanical flexibility are demonstrated. It is believed that the high-kdielectric copolymer films presented in this study will be an important guideline to develop future flexible, wearable electronics.