Influence of acrylic acid grafting of isotactic polypropylene on the dielectric properties of the polymer is investigated using density functional theory (DFT) calculations, both in the molecular modeling and three-dimensional (3D) bulk periodic system frameworks. In our molecular modeling calculations, polarizability volume, and polarizability volume per mass which reflects the permittivity of the polymer, as well as the HOMO-LUMO gap, one of the important measures indicating the electrical breakdown voltage strength, were examined for oligomers with various chain lengths and carboxyl mixture ratios. When a polypropylene oligomer is grafted with carboxyl groups (cf. acrylic acid), our calculations show that the increase of the polarizability volume α' of the oligomer is proportional to the increase of its mass m, while the ratio α'/m decreases from the value of a pure polymer when increasing the mixture ratio. The decreasing ratio of α'/m under carboxyl grafting indicates that the material permittivity might also decrease if the mass density of the material remains constant. Furthermore, our calculations show that the HOMO-LUMO gap energy decreases by only about 15% in grafting, but this decrease seems to be independent on the mixture ratio of carboxyl. This indicates that by doping polymers with additives better dielectric properties can be tailored. Finally, using the first-principles molecular DFT results for polarizability volume per mass in connection with the classical Clausius-Mossotti relation, we have estimated static permittivity for acrylic acid grafted polypropylene, assuming the structural density keeping constant under grafting. The computed permittivity values are in a qualitative agreement with the recent experiments, showing increasing tendency of the permittivity as a function of the grafting composition. In order to validate our molecular DFT based approach, we have also carried out extensive three-dimensional bulk periodic first-principles total-energy calculations in the frameworks of the density functional theory and density functional perturbation theory (DFPT) for crystalline acrylic acid grafted polypropylene. Interestingly, the computed electronic and dielectric properties behave very similarly between the simplified molecular DFT modeling and the more realistic 3D bulk periodic DFPT method. In particular, the static permittivity values [ε(r)(0)] from the molecular DFT-Clausius-Mossotti modeling are in excellent agreement with the high-frequency dielectric constant values (ε(∞)) from the DFPT method. This obviously implies that the chain-to-chain interaction to dielectric and electronic properties of acrylic acid polypropylene, to a first approximation, can be neglected, therefore justifying the usage of molecular DFT modeling in our calculations.