The study of recent literature reveals that the discovery of high TC (TC = 39K) superconductivity (SC) in MgB2 has generated considerable interest in this binary system. The appearance of high TC SC in such a simple system which does not contain transition metals has led to considerable optimism among workers. The phonon mediated BCS type mechanism has been acknowledged to be a good tool for its theoretical study viaMcMillan formalism. Recent studies are the milestones in this direction. In this paper, we report the HarrisonÂs First Principle Pseudopotential (HFPP) study of this system so as to bring out the effectiveness of this technique which has not been explored as yet. It has been observed that due to the unique double layered structure ofMgB2 some adjustable parameter is to be introduced in the computation of the form factor so as to predict the SC parameters in reasonable agreementwith experiment.