In this work, the effect of oxygen doping on the critical parameters of the mercury based superconducting sample such as critical transition temperature, T-c, critical magnetic field, H-c, critical current density, J(c), has been investigated by the magnetic susceptibility versus temperature (chi-T) and magnetization versus applied magnetic field (M-H) measurements and, X-Ray Diffraction (XRD) patterns. It has been observed that regardless of the oxygen doping concentration, the mercury cuprate system possesses two intrinsic superconducting phases together, HgBa2Ca2Cu3O8+x and HgBa2CaCu2O6+x. However, the highest T-c has been determined for the optimum oxygen doped sample. Moreover, it has been revealed that superconducting properties, crystal lattice parameters, coherent lengths, xi(ab), xi(c) and the anisotropy factor gamma etc. are very sensitive to oxygen doping procedures. Hence, the results presented this work enables one to obtain the mercury based superconductor with the most desirable criticals and other parameters for theoretical and technological applications by arranging the oxygen doping concentration.