In this paper the relative permittivity response of some nanometals such as Gold (Au), Silver(Ag), Copper(Cu), Aluminum (Al) and Nickel(Ni) are investigated at optical frequencies. The permittivity response is necessary because the optical response of the metal nanoantenna highly depends on the permittivity of the metals. The surface plasma response largely depends on the permittivity response at optical frequency. This relative permittivity response also playsan important role in the design process of a nanoantenna. This paper represents the permittivity response at the frequency range of 20–300 THz (the wavelength range of 3–15 μm).