Polymer/CNT (carbon nanotube) composites with a high dielectric constant show great potential for energy storage applications. However, these CNT-based composites usually suffer from high dielectric loss and low breakdown strength, and pose difficulties in the tailoring of the dielectric constant. The integration of a CNT cladding insulator filler layer into the polymers provides an effective way to reach a low dielectric loss and a high breakdown strength. But the insulator layer could significantly reduce the dielectric constant, thereby decreasing the energy storage density of composites. Herein, we have designed and fabricated a novel candidate composed of a semiconductor NH₂–CuPc coated multi-walled carbon nanotube (MWCNT-CuPc) through chemical grafting, in which dielectric CuPc layers can act not only as insulation barriers for suppressing leakage current, but also as semi-conductor layers to partially block electron motion. Thus the as-prepared composites exhibit not only a higher dielectric constant but also extremely decreased dielectric loss and excellent dielectric strength. Moreover, the dielectric properties of the composites can be easily tuned by tailoring the loading of MWCNT-CuPc. Our strategy provides a new pathway to achieve polymer/CNT composites with high dielectric performances for energy storage applications.