The models of the high angle grain boundaries with different Σ(5,9,11) of pure aluminum and the interface between carbon nanotube and pure aluminum were constructed by the self-developed computer software. The electronic structures (structure energies of aluminum grain boundaries,the interfaces between carbon nanotube and pure aluminum,carbon nanotubes and fermi levels of different systems, etc.) of the carbon nanotube reinforced aluminum matrix composites were calculated with Recursion method. The calculated results show that the structure energy of the aluminum high angle grain boundary with Σ=5 is the lowest, it is t