The geometrical and electronic structures, the dopant formation energies, lattice constants, band structure and density of states of p-type SiC are calculated by the first principles of plane wave ultra-soft pseudo-potential method based on density functional theory. The band structures of different concentrations of B, Al and Ga are calculated. The results of the electronic structure show that the band gap narrows with the increase of doping concentration of B and the band gap widens with the increase of doping concentration of Al and Ga. At the same concentration the band gap of Ga doped SiC is wider than that of Al doped SiC, the band gap of Al doped SiC is wider than B doped SiC.