Functionalization of carbon nanotubes (CNTs)is considered as an essential step to enable their manipulation and application in potential end-use products. In this paper, novel ternary dielectric polymer-based nanocomposite films, consisting of hyperbranched copper phthalocyanine grafted carbon nanotubes and polyarylene ether nitriles (PEN/HBCuPc-g-CNTs), were prepared via solution-casting method. The CNTs are enwrapped by a functional intermediate HBCuPc thick layer and formed rough shell on the surface of CNTs to ensure a good dispersion of CNTs in PEN matrix and suppress the mobility of free charge carriers effectively, resulting in significant improvement of the dielectric properties of PEN/HBCuPc-g-CNTs nanocomposite films in contrast to PEN/CNTs. Furthermore, around 38 wt% of phthalocyanine oligomer based on the total weight of the CNTs can be covalently grafted to the surface of the CNTs. Compared with raw CNTs, grafted CNTs showed better dispersion and stronger interfacial adhesion to PEN matrix. SEM images showed that HBCuPc-CNT was perfectly embedded in the matrix and no pullout phenomenon could be observed, thus resulting in significant improvement of the mechanical and thermal properties of PEN/HBCuPcg-CNTs nanocomposite films compared to pure PEN films. For 2.0 wt% HBCuPc-g-CNTs reinforced PEN nanocomposite films, the tensile strength and T g were increased by 24.5 % and 5°C, respectively, in comparison with those of pure PEN.