In this paper we report on ab initio pseudopotential density-functional calculations of some possible high-pressure phases of carbon. The total energies of several hybrid diamond-graphite structures were calculated as a function of volume using density-functional theory and the local density approximation. The lowest calculated transition pressures between hexagonal-graphite and hybrid structures were 17 and 20GPa, which compare well with the experimental value of 14GPa for the transition at low temperatures between graphite and a still unidentified hard transparent phase. The electronic densities of states for the different structures are presented. Also, the x-ray powder diffraction patterns for a few structures were simulated and qualitatively compared to published experimental diffraction patterns.