In this work, the dielectric property of a nanocomposite (NC) consisting of silver nanoparticle and E7 liquid crystal (LC) has been investigated theoretically at different temperatures. The study shows that the surface plasmon resonance (SPR) and filling fraction of the silver nanoparticle significantly change the dielectric property of the NC. To study the optical property of the defective periodic structure, the NC was considered as a defect layer in a semifinite one-dimensional periodic structure (1DPS) of $\rm{TiO_{2}}$ and $\rm{SiO_{2}}$ layers, i.e. $\rm{(TiO_{2}|SiO_{2})^{5}|NC|(TiO_{2}|SiO_{2})^{5}}$. The optical properties of the 1DPS with the NC as the defect layer have been studied by the simple transfer matrix method (TMM). Moreover, the transmission and absorption characteristics of the 1DPS in the presence of silver nanoparticle in the NC have been studied with different orientations of the LC molecule.