Some superconducting parameters of the high temperature superconductors, such as the plasma frequency and the critical transition temperature, depend on the oxygen content of the material. Since the oxygen content is effective on the grain size of the system, the under, optimally and over oxygen doped Hg-based copper oxide layered superconductors, which have the hole type superconductivity, have been investigated in this study. As is known that the concentration of hole type carriers is increased via optimally oxygen annealing. In other words, relatively higher values for the various critical parameters are achieved by the optimally oxygen doping procedure. In this work, the grain sizes of the oxygen annealed samples have been investigated by Scanning Electron Microscopy (SEM). Moreover, the magnetization data obtained via Superconducting Interference Quantum Device (SQUID) has been utilized for calculation of critical current density, which is essential parameter for determining Josephson penetration depth. The Josephson penetration depths of the systems have been calculated by Lawrence-Doniach Model for high temperature superconductors. Since plasma frequency of the system is inversely proportional to Josephson penetration depth, the plasma frequencies of the various doping profiles have also been calculated for the high temperature superconductor investigated. (C) 2013 Elsevier B.V. All rights reserved.