The electronic, magnetic, and mechanical properties of CaCu3V4O12 are investigated by use of the density functional theory method. The calculated results indicate that CaCu3V4O12 is a half-metallic and ferrimagnetic compound. The magnetic coupling for Cu-V is antiferromagnetic, while those for Cu-Cu and V-V are ferromagnetic. The obtained elastic constants suggest that the compound is mechanically stable. The calculated oxidation states and density of states reveal the existence of a mixed valence for Cu and V. This supports the experimental observation of the mixed valence in Ca2+Cu2+Cu2+(V25+V24+)O-12.