Graphene has attracted lots of researchers attention because of its remarkable conductivity in both electrically and thermally. However, it has poor dispersibility in organic solvents which limited its applications. Polymers with aromatic end group which act as an intercalator were prepared by ring-opening polymerization with ε-caprolactone by utilizing 1-naphthalene methanol (1-NM) as an initiator. These intercalators will exist between graphene oxide (GO) sheets to prevent aggregation via interactions. The attachment of 1-NM on polymer chains was supported by ultraviolet-visible spectra, size exclusion chromatography profiles, and 1H nuclear magnetic resonance spectra. Exfoliated structured functionalized GO (fGO)/polycaprolactone (PCL) (synthesized fGO) nanocomposites that dispersed well in acetone, chloroform, N,N-dimethylformamide, dimethyl sulfoxide, tetrahydrofuran, and toluene were successfully synthesized. This agreed well with the enlarged interlayer spacing in the optimized fGO as compared to that of GO from density functional theory simulations using the DMol3 module that implemented in the Materials Studio 6.0. Furthermore, its potential to be applied as green electronics in electronics, aerospace, and automotive industries was presented, by trailering the thermal conductivity enhancement from the incorporation of fGO/PCL with commercialized biodegradable polymers, PCL, and poly[(R)-3-hydroxybutyric acid].