Despite many studies have been carried, there is no clear understanding of the growth mechanism involved in the high-pressure and high-temperature (HPHT) diamond synthesis with metal catalyst, especially the problem about carbon source. In this paper, the lattice constants of diamond, graphite and Fe3C at HPHT were calculated with the linear expansion coefficient and elastic constant. Then based on the empirical electron theory of solids and molecules (EET), the valence electron structures of them and their common crystal planes were calculated, and the boundary condition of electron movement in the Thomas-Fermi-Dirac theory modified by Cheng (TFDC) was applied to analyzing the electron density continuity of the interface. It was found that the relative electron density differences across graphite/diamond interfaces are great and discontinuous at the first order of approximation, while the relative electron density differences across Fe3C/diamond interfaces were continuous. The results show that the carbon atom cluster is easier to decompose from Fe3C than from graphite and to transform into diamond structure, so the carbon source for diamond crystal growth may come from the decomposition of Fe3C instead of graphite. Accordingly, the diamond growth mechanism was analyzed from the viewpoint of valence electron structure.