LaB6 nanoparticles are widely used as solar control materials for strong near-infrared absorption and high visible transparency. In order to elucidate the origin of this unique optical property, first-principles calculations have been made for the energy-band structure and dielectric functions of R(III)B6 (R(III) = Sc, Y, La, Ac). On account of the precise assessment of the energy eigenvalues of vacant states in conduction band by employing the screened exchange method, as well as to the incorporation of the Drude term, dielectric functions and various physical properties of LaB6 have been reproduced in excellent agreement with experimental values. Systematic examinations of dielectric functions and electronic structures of the trivalent metal hexaborides have clarified the origin of the visible transparency and the near-infrared plasmon absorption of R(III)B6 nanoparticles.