The possibility of obtaining relatively high dielectric constant polymer-metal composite by incorporating silver nanoparticles in a polypropylene (PP) polymer matrix by grafting and successive reduction method was demonstrated. Frequency and temperature dependence of AC conductivity and dielectric constant (ε') and dielectric loss (ε'') in pure polypropylene, PP-g-(AAc-co-Sty), and PP-g-(AAc-co-Sty)-Ag nanocomposite are studied in the frequency range 50 Hz- 5 MHz and in the temperature range 30- 70 oC. The experimental results show that the polarity of PP is weak due to deficiency of polar groups. The values of ε' and ε'' increased dramatically with the addition of silver nanoparticles in polypropylene. The obtained AC conductivity is follow the correlated barrier-hopping model (CBH) since the frequency exponent (s) and AC conductivity are both frequency and temperature dependent. The calculated value of maximum barrier height Wm for PP-g-(AAc-co-Sty)-Ag is 0.242eV. The dielectric relaxation process are studied in respect of the electric modulus formalism.