The 4f-shell electrons of rare-earth ion R have a certain influence on both the electrical and optical properties of RInO 3 . We have studied the electronic structures, optical and dielectric properties of hexagonal compounds RInO 3 (R = Dy, Ho, and Er) by performing first principles calculations. After optimization, the lattice parameters are in great agreement with the experiment with an error within 1%. Band structure calculations reveal decreasing band gaps with the increase of atomic number, yielding the highest conductivity for ErInO 3 , which has the smallest band gap in the present study. We have calculated the density of states of RInO 3 and characterized the displacement of In and O. The dielectric properties and ionic contribution have been calculated and a detailed comparison has been made on the dielectric function including the static dielectric tensor. The absorption coefficient, the reflectivity, the refractive index, the conductivity and the electron energy-loss spectrum of hexagonal DyInO 3 , HoInO 3 and DyInO 3 have been calculated and analyzed.