In this study, Styrene-Ethylene-Butylene-Styrene terpolymer was mixed with certain amounts of Maleic Anhydride and Dicumil Peroxide using an internal mixer to graft Maleic Anhydride onto the terpolymer. Afterwards, different weight percentages of silica nanoparticles and the grafted polymer were added to the terpolymer and mixed using internal mixer. At the next step, mechanical properties of each sample were compared to other samples. The optimum grafting percentage was reached at 3 wt.% of Maleic Anhydride and 0.11 wt.% of Dicumil Peroxide. It was observed that the hardness of samples with higher amounts of silica nanoparticles was 17% more than the other samples. Also tensile tests showed that by increasing the amount of nanoparticles to a certain degree, mechanical strength will increase and after that it will decrease. It is noteworthy that samples having 3 phr of nanoparticles had higher alongation at break values. TEM images showed that samples with 3 phr silica nanoparticles had the best dispersion. In addition, the peaks assigned to carbonyl groups have been observed in FTIR spectra and showed that maleic anhydride is grafted successfully to the terpolymer. Keywords: Nanocomposite, SEBS, Silica Nanoparticles, Compatibilizer;