Recent research in developing novel lead electrodes composed of carbon and lead composites have shown potential of increasing the ability of lead-acid batteries to store energy in grid scale applications but many technical challenges persist. One challenging obstacle is that influence of carbon on lead matrix in these new battery systems are obscure and the mechanism taking place at the atomic level is difficult to investigate experimentally. However, a better understanding of the working mechanisms of battery materials is crucial for developing new advanced batteries toward industrial applications. In this paper the density functional theory (DFT) calculation are carried out using the Vienna Ab-initio Simulation Package (VASP) with spin-polarized generalized gradient approximation (GGA) functional parametrized by Perdew, Burke, and Enrzerhof (PBE) is used to describe the exchange and correlation energies of the electrons. Herein, a systematic increase in system site with decrease in C concentration was investigated in Pb using DFT. This study provides vital fundamental data on Pb-C structure such as density of states, band structures, defect formation energies.