Here we report a facile approach to enhance the dispersibility of ethylene vinyl acetate copolymer (EVA)/silica nanocomposites (for the EVA/silica nanocomposites and interaction between silica nanoparticles (nanosilica) and EVA by adding EVA-g-acrylic acid (EVAgAA) as a compatibilizer, which was formed by grafting acrylic acid onto EVA chains with the aid of dicumyl peroxide). The above nanocomposites with and without EVAgAA were prepared by melt mixing in a Haake intermixer with different contents of silica and EVAgAA. Their structure and morphology were characterized by Fourier transform infra-red (FT-IR) spectroscopy, field emission scanning electron microscopy (FE-SEM), and the mechanical, rheological, dielectrical, and flammability properties of the nanocomposites were also investigated. The FT-IR spectra of the nanocomposites confirmed the formation of hydrogen bonds between the surface silanol groups of nanosilica and C=O groups of EVA and/or EVAgAA. The presence of EVAgAA remarkably increased the intensity of hydrogen bonding between nanosilica and EVA which not only enhanced the dispersion of nanosilica in EVA matrix but also increased the mechanical, viscosity and storage modulus of EVA/silica nanocomposites. In addition, the flammability of EVA/silica nanocomposites is also significantly reduced after the functionalization with EVAgAA. However, the mechanical properties of EVA/silica nanocomposites tended to level off when its content was above 1.5 wt.%. It has also been found that the dielectric constant value of the EVA/EVAgAA/silica nanocomposites is much lower than that of the EVA/silica nanocomposites, which is another evidence of the hydrogen bonding formation between EVAgAA and nanosilica.