In the present work, the electronic band structure and optical properties of RE2(MoO4)(3) are investigated. The ground state energies and electronic structures were calculated using density functional theory(DFT) within the generalized-gradient approximation (GGA). The real and imaginary parts of dielectric functions and hence the optical functions such as energyloss function, the effective number of valance electrons and the effective optical dielectric constant were also calculated. The main structure element in all our of compounds is the Moat tetrahedron. The presence of the MoO(4 )tetrahedra in the lattice of Gd-2(MoO4)(3), the similarity of the band structure and optical spectra of Gd-2(MoO4)(3) to those other tetraoxyanions of molybdenium demonstrate an important role of the MoO(4)tetrahedra in the formation of the energy spectrum of Gd-2(MoO4)(3) and other RE2(MoO4)(3) compounds. This means that the MoO(4)tetrahedra determine the lower edge of the conduction band and the upper edge of the valence band, and the conduction band is split into two subbands. The optical properties of RE2(MoO4)(3) are in good agreement with this conclusion and previous experimental data.