By use of the structural parameters of the single crystal lithium indium orthoborate obtained by Penin et al. (Solid State Sci. 2001, 3, 461-468), from X- ray diffraction data, we present a first-principle study of the electronic structure and the linear optical properties for the novel lithium indium orthoborate Li3InB2O6. A full-potential linear augmented plane wave method within density functional theory with the Engel-Vosko exchange correlation was used. This compound has a wide direct energy band gap of about 3.8 eV with both the valence band maximum and conduction band minimum located at the center of the Brillouin zone. Our calculations of the partial density of states shows that the upper valence band originates predominantly from the O-p, B- p, and In-p states, and the lower conduction band is dominated by the O-s/p, In-p, and B-p states. Thus the O-p states in the upper valence band and lower conduction band has a significant effect on the energy band gap dispersion. The uniaxial anisotropy [deltaepsilon=(epsilon0zz-epsilon0xx)/epsilon0tot] is about -0.041.