In this study, the influence of interfacial layers, in addition to other effective parameters, on the dielectric efficiency of polymer nanocomposites in the rubbery state is presented. For this purpose, reduced graphene oxide (rGO) was grafted by poly (butyl acrylate) chains (rGO-PBA) via surface-initiated atom transfer radical polymerization (SI-ATRP) and incorporated into an acrylic co-polymer matrix with the glass-transition temperature (Tg) well below room temperature. The rGO exhibited poor dispersion and uneven distribution in acrylic co-polymer, whereas polymer grafted-rGO showed excellent dispersion. The grafted chains can penetrate and form entropic interactions with the matrix chains, which results in a strong interfacial region. The immobilized interfacial layer was characterized by DSC and dielectric measurements. The dielectric measurements in different temperatures provided the means to evaluate the contribution of the interfacial layers on dielectric properties. The findings confirmed that there exists an optimum chain mobility in which the chain polarization shows a major contribution to the dielectric properties of polymer nanocomposites. Reduction of temperature to a certain degree exhibited more rise in the dielectric properties of polymer/rGO-PBA nanocomposites than pure matrix which can be correlated to the interfacial region.