In this study, the AC impedance, the complex dielectric function, and the complex electric modulus properties of mercury based copper oxide layered cuprates, which have superconducting properties below the critical transition temperature, have been investigated at room temperature. The HgBa2Ca2Cu3O8+x samples were synthesized by a conventional, solid state reaction preparation method with an identical stoichiometric ratio. The varied oxygen content of the sample was obtained by oxygen annealing. The AC impedance and the related dielectric and electric modulus properties of non-oxygen doped (i.e. as grown) and optimum oxygen doped HgBa2Ca2Cu3O8+x samples, was measured by an impedance analyzer at room temperature within the frequency interval of 10 Hz-10 MHz. AC impedance spectroscopy analyses of the samples suggest Koop's bilayer model for the structure of Hg-based perovskites. Additionally, the optimally oxygen doped process increased grain and grain boundary resistance along with decreasing grain size. Moreover, AC conductivity results have also confirmed the increased resistive behavior of the sample due to oxygen doping. Furthermore, complex dielectric function analyses have determined an oxygen doping induced negative dielectric constant for the mercury cuprates. In this context, optimally oxygen doped mercury cuprate has a promising potential for metamaterial coating applications.