Global Equation of State models are used to carry out hydrodynamic calculations of inertial confinement fusion systems. There are some such models like QEOS which are used quite routinely in ICF simulations. The empirical content of QEOS, which otherwise does have a strong theoretical basis, provides scope for further research aiming at making the EOS theoretically more sound by reducing the empirical nature of the EOS. To this end, we have made some progress by developing an equation of state which uses a more accurate form for the zero temperature isotherm and a method to calculate the Grüneisen parameter so as to yield an ion equation of state which is better than the Cowan's model used in QEOS. The parameters of the model are taken from experiments or electronic structure calculations. The EOS is verified against the shock Hugoniot data and the melting data of Pb and U, and the phase diagram and Hugoniot of Hf. The stability analysis of some metals like Cu and Mo had also be.